# Z Score Table Calculator

How to use Z table: The values inside the given table represent the areas under the standard normal curve for values between 0 and the relative z-score. 95 I should get 1. Using the R score calculator to calculate your R score: Enter the information required in the fields bellow and press the Enter key or on the button "Add class" to calculate the R score for this class. Z-scores can be found in a table, but using a TI-84 Plus calculator is easier and more accurate. Z Score formula. First, use the Z-table to find the value where the row. 8%! ex Find the proportion with z-score above 1. That's because we're going to see how much of the area lies above the point (i. 5 percent (. Now, therefore, the upper z-score will be z = 1. How can I calculate the z score on my casio fx-115ES plus calculator? I need to know for statistics. Negative Z score table Use the negative Z score table below to find values on the left of the mean as can be seen in the graph alongside. 4 standard deviations below the mean. If he was below the mean, it would be a negative. Applets: A good applet for showing the correspondence between raw data and z-scores by Gary McClelland is linked here (you need to hit enter after entering your. View Homework Help - Homework 4 from PS 307 at Park University. This data is also used to create dynamic z-score tables. 27); this negative z-score suggests that compared to the other women in the study, Celia does not value high salary as a very important characteristic in a partner. 9332, and the area in the tail is. Student t-Value Calculator. Z-Score Formula. The point where the row & column meets for the corresponding z-score value is the critical value of Z or the rejection area of one or two tailed z-distribution. A z-score is a standardized score that describes how many standard deviations an element is from the mean. In statistics, a Z score is the number of standard deviations a data point appears on a standard distribution curve of the entire dataset. It is an excel spreadsheet requiring the use of macros but will automatically pull data from the internet and let you calculate the Altman Z Score with this free spreadsheet. Suppose!apopulation!was!normally!distributed!with!amean!of!10!and!standard!deviation!of!2. R Score is a statistical method used by Quebec colleges. When diagnosing learning disabilities in school-age children, school psychologists typically look for a significant gap between the student's score on an aptitude, or cognitive, measure and (lower) performance on academic achievement testing. Z-Test Calculator for 2 Proportions. A z score table is used in hypothesis testing to check proportions and the difference between two means. Just enter your raw score, population mean and standard deviation, and hit "Calculate Z". So, the z score here, z score here is a positive 2. In the 5th edition, Table B. The goal of calculating a z - score is to relate a particular normal distribution to the standard normal distribution. This z-score corresponds to the 58th percentile. Add new tag Algebra Algebra 1 Algebra answers Algebra Help Algebra problems Calculus Chemistry common core assessments common core math standards common core standards common core state standards education English essay Essay Writing Force genetics Geometry H. A false positive (i. Compare the z-scores. In statistical inference, we are interested to know whether a small sample comes from a population. hypothesis hypothesis testing Independent Learner Inorganic Chemistry. $z = \frac{X-\mu}{\sigma}$ This is exactly what this z score calculator with steps will do for you if you type the parameters in the form above. This calculator will tell you the normal distribution Z-score associated with a given cumulative probability level. You can use our z-score calculator to determine this value for you. 6 in our example). For any given value of z, this page will calculate the respective one-tailed probabilities of —z and +z; the two-tailed probability of±z; and the proportion of the normal distribution falling between —z and +z. The Z-score normalized value equals (the original column value minus the mean column value) divided by the standard deviation of the column values. If you use the first, and put in, say, z = 2, it will tell you that the probability to the left is 0. In statistics, a Z score is the number of standard deviations a data point appears on a standard distribution curve of the entire dataset. The z table is a table of probabilities for each z value (a z value is the number of standardized deviation you are from the mean). If he was below the mean, it would be a negative. Cpk = (USL. Look at the graph. 5 down to 1. 9), This means we are going subtract the area under the curve that is to the left of the z score 3. Cpk = (USL. 025 is z = −1. So, the z score here, z score here is a positive 2. Z Table Score Calculator allows you to quickly calculate z-scores. 32% of students scored lesser than Jack. This is very easy: just stick your Z score in the box marked Z score, select your significance level and whether you're testing a one or two-tailed hypothesis (if you're not sure, go with the defaults), then press the button!. The significance of the correlation coefficient is calculated by using a single sided t-test, following Cohen. 1 Calculate z-score when Mean and Standard Deviation are given. The Z-Score is a formula consisting of four to five weighted financial ratios (incorporating information from both the balance sheet and income statement). Coronary Artery Z-Scores. 5 it is interpreted as "+2. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. 99 to 0 on the left side and 0 to 3. If you want to calculate the p-value, you have to find the integral with lower limit equal to the z-score and upper limit equal to infinity. The z-score provides a simple measure by which different measures can be compared in terms of their deviation from the mean. This is very easy: just stick your Z score in the box marked Z score, select your significance level and whether you're testing a one or two-tailed hypothesis (if you're not sure, go with the defaults), then press the button!. If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator. given something called a z-score. In statistics, the z-score (or standard score) of an observation is the number of standard deviations that it is above or below the population mean. The standard normal distribution has been well-studied, and there are tables that provide areas underneath the curve, which we can then use for applications. What is a Z-score? A z-score shows you the distance between an observed score and the mean in units of standard deviations. Z-score a composite score, summarizing the weighted results of a number of ACCOUNTING RATIOS, that claims to predict a company's likelihood of failure. Appendix Tables A3 T ABLE 3 Binomial Pr obability Distribution C n, r p r q n r This table shows the probability of r successes in n independent trials, each with probability of success p. 45, move along the area in the table and locate the nearest value. You just need to enter a raw score, population mean and standard deviation, and hit "Calculate". Tables • T-11 Table entry for p and C is the critical value t∗ with probability p lying to its right and probability C lying between −t∗ and t∗. The Z score, the number resulting from the calculation, indicates where you fall in the range of body fat measurements. This table covers children between 0 and 60 months of age, but you can modify the table as needed for your project. The Z-Score Calculator uses the following formula: z = (x - μ) / σ. If we normalize the data into a simpler form with the help of z score normalization, then it's very easy to understand by our brains. If it is on the right-hand side, we will have a positive value of z else negative. qThe Z -score is expresses the number of standard deviations the value x is from the mean qA negative Z -score implies that x is to the left of the mean and a positive Z -score implies that x is to the right of the mean Z Score Equation z = x - x s For a score of 83 from the aptitude data set, z = = 1. Return to Statistics Topics. Z-score calculator, p-value from z-table, left tail, right tail, two tail, formulas, work with steps, step by step calculation, real world and practice problems to learn how to find standard score for any raw value of X in the normal distribution. So, here we go. Right Tailed Test. Looking at the table we know P(z <= 3. consider whether z is positive or negative when using the table. Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals). Now, we use the z table to find the percent (or probability) that a person would have an IQ of 120 or less, which is the same as the percent (or probability) that a z score is 1. z scores are assumed to have come from a normal population with mean zero and standard deviation one. Please enter the necessary parameter values, and then click 'Calculate'. 475) is at z=1. 751: 37-0. For George’s example we need to use the 2nd table as his test result corresponds to a positive z-score of 0. Z-Scores Can Help Us Understand… How typical a particular score is within bunch of scores. If I have a z-score, I can look up the probability in a distribution table. Altman, who was, at the time, an Assistant Professor of Finance at New York University. Now, therefore, the upper z-score will be z = 1. It is an excel spreadsheet requiring the use of macros but will automatically pull data from the internet and let you calculate the Altman Z Score with this free spreadsheet. Z Score Table- chart value corresponds to area below z score. The z-score corresponding to a left-tail area of 0. 27 for your math score. –z 0 z The area remaining in the tails is. Click for Normal Data Table; National health and nutrition survey (NHANES), CDC/National Center for Health Statistics. This formula allows you to calculate a z-score for any data point in your sample. Most z-tables show the area under the normal curve to the left of z. This page allows you to calculate the probability of chance occurrence of a given z, or to calculate z given a probability Q. To use Table A: ! Find the corresponding z-score. 08 and the standard deviation was 3. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Let Z be a standard normal random variable, Use the calculator provided to determine the value of c such that P ( c < Z < c-1. The procedure is not very good for estimating large z-values. Percentiles are provided for Z Scores between -3. 1) calculate the z-score, then find the absolute value of the z-score in column a 2) if the z-score is positive, automatically add 0. If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator. P Value from Z Score Calculator. Determine z-scores for the mitral valve, aortic valve, tricuspid valve, and pulmonic valve using this calculator. You can easily calculate a z-score on a TI-83 calculator or in Excel. There is in depth information on the calculator and the results provided below the form. , z score) that corresponds with Y = 120. Padua Score <4: Low risk of VTE. Since the z-score is a positive number, we look at the Positive Z-Score table for the percent of students who scored within 1. • compute a z-score for a value given that value, its mean, and it's standard deviation. Minitab would calculate a z-score of -1. To convert from an IQ score to a z score, we use the formula: The z score for your IQ of 120 is 1. I have numpy, statsmodel, pandas, and scipy(I think) How do I calculate the z score of a p-value and vice versa? For example if I have a p value of 0. The z- is a N(0, 1) distribution, given by the equation: The area within an interval (a,b) = normalcdf(a,b) = (It is not integrable algebraically. Click on the table below to go to a page from which the table may be printed. If we look this z-score (1. Standard normal distribution table is used to find the area under the f(z) function in order to find the probability of a specified range of distribution. It shows you the percent of population: between 0 and Z (option "0 to Z") less than Z (option "Up to Z") greater than Z (option "Z onwards") It only display values to 0. 5?! With!proportion,!we!can. 96, by the symmetry property of the standard normal distribution. 30 and the column labeled 0. The Altman Z Score. Carry your. To use the table, which is easier than it might look at first sight, we start with our z-score, 0. A Z-Score is a statistical value that tells you how many standard deviations a particular value happens to be from the mean of the entire data set. In A/B Testing terms, all of your visitors are observations, and the Control experience makes up a bell curve. How can I calculate the z score on my casio fx-115ES plus calculator? I need to know for statistics. Features & Benefits Get the exact area: No need to try and interpret hard-to-read z-score tables. 5 down to 1. If he was below the mean, it would be a negative. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. The given value is significance level. You can learn more about accounting from the following articles – Mortgage Calculator in Excel; Mortgage APR vs Interest Rate – Compare. If data are normally distributed, approximately 95% of the data should have Z-score between -2 and +2. Z is the same size as X. Remember that a z-score is a standard score (also called the standard Gaussian variable) that is calculated by subtracting the mean from a value and dividing the result by the standard deviation: z = (value - mean)/standard deviation. Notice the inequality points to the right. 45, we go to the table and look at where. Normal Distribution Calculations Using Technology All of the calculations that we will do in Math 180A involving the normal distribution can be done using tables. 71 : 2nd -2. We have to find its corresponding confidence level. USING MINITAB INSTEAD OF TABLES As you can see from the table, the answer is 0. This bone mineral density for bone fracture calculator assesses fracture risk in the following five years based on patient age, BMD T score and personal factors. Z tables indicate what percentage of the statistics is under the curve at any given point. How can I calculate the z score on my casio fx-115ES plus calculator? I need to know for statistics. Z score table and calculation z score table t z score table and calculation z score table and calculation Whats people lookup in this blog: Negative Z Score Table Calculator. Enter required numbers for the population mean and the standard deviation and hit Calculate. The idea here is that the values in the table represent area to the left, so if we're asked to find the value with an area of 0. A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. 0 versus ZA=4. $p = \Pr(Z z^*)$ How do we find such $$z^*$$? The idea is to a percentile to z score conversion table, which is essentially using a standard normal distribution table. A score that is 30 points below the mean. This data is also used to create dynamic z-score tables. 1) Use the normal distribution table (Table A-2 pp. Z = zscore(X) returns the z-score for each element of X such that columns of X are centered to have mean 0 and scaled to have standard deviation 1. Notice the inequality points to the right. It does not change the shape of the distribution! Raw score does not change into a bell shaped curve when changed into standard scores. PSYCHOMETRIC CONVERSION TABLE Standard Score Percentile Rank Scaled Score ETS Score T-Score Z-Score Description 89 23 Low Average 88 21 425 42 -0. 18 Using the z table in Appendix B, calculate the following percentages for a z score of 1. The Boston Children's Hospital Z-Score Calculator allows for the calcuation of the standard score (z-score) of various regressions based on data gathered over the past 12 years on normal children. What’s Next? Calculating Z Score manually and finding the probability in Standard Normal Table is only for you to learn the concept, you can get the value quickly using SPSS and Excel. I do not have the Z values. Corresponding values which are less than the mean are marked with a negative score in the z-table and respresent the area under the bell curve to theContinue Reading. After calculating the standardized score, we need to look up the area (same as probability) using the z-table. The z score is the numerical value which represents how many standard deviations a score is above the mean. of the table shows the proportion of values to the left of each !-value. But why? Let's look at the equations: A z score is the same as a standard score; the number of standard deviations above the mean. Features & Benefits Get the exact area: No need to try and interpret hard-to-read z-score tables. Create a blank Excel worksheet, copy the following table, select cell A1 in your blank Excel worksheet, and then paste the entries so that the table fills cells A1:C24 in your worksheet. The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a non-federal website. z-tables for the standard normal distribution. Get a Z score for normally distributed data using this online calculator. To find the z value for 0. An introductory statistics text for the social sciences. Z score table and calculation z score table t z score table and calculation z score table and calculation Whats people lookup in this blog: Negative Z Score Table Calculator. Z-Score to Percentile Calculator Enter a z-critical value and get the area under the normal curve (a percentage). First, use the Z-table to find the value where the row. Since the z-score is negative and we want the area below that point we will be using the tail area. For negative values just add a “-” sign. Z Score Calculation is a important aspect of six sigma projects. 5 indicates osteoporosis. This concept was adapted to the business and finance world by Dr. 354 std devs above the mean. 5 standard deviations above the mean. The table includes positive z statistics (from 0. Refer the column & row values for z-score. 11 would be in the 14th percentile. Just enter your p-value, which must be between 0 and 1, and then hit the button below. Calculate test statistic 0. The raw score computed is the actual score, or value, obtained. Calculating Z-Score; Calculating Z-Score in SQL. For use in Georgetown University statistics classes: Math-006 and Math-040. 0 versus ZA=4. Use this Z to P calculator to easily convert Z-scores to P-values (one or two-tailed) and see if a result is statistically significant. 49 would be the intersection of 0. 29 (add the 0. First move to the left extreme find the value in the z column. 36, look in the intersecting cell for the row labeled 2. The z-score provides a simple measure by which different measures can be compared in terms of their deviation from the mean. 2 is on page App17. Using the Weight/Height table to calculate the Weight-for-Height/Length percentage or Standard Deviation (Z-score). The Altman Z score was formulated by a professor in 1968 to predict. Calculate Z (two tailed) from Confidence Level To determine the Z value, enter the chosen Confidence Level in the box below and press the Return key or the Calculate button. Extensions and Connections (for all students) Give students the mean and standard deviation of a data set in addition to a z-score, and ask them. Enter a value, population mean and the standard deviation (for the population). You can look up the t-value for a desired level of confidence in a t-distribution table, given the degrees of freedom (n – 1) associated with your sample. You can use our z-score calculator to determine this value for you. Using a Graphing calculator to use a Z-table Finding % given bounds (for a non-standard normal) normalcdf( can be used to give you the % between a lower and upper bound for a non-standard normal (i. ¨ If your Z score is negative, subtract the value in Table A. Coronary Artery Z-Scores. A Z score can be determined by multiplying the Ppk score by 3. Find a critical value in this T value table >>>Click to use a T. Bottom 15% low $$customers (z-score of the dollar_amt variable less than -1). So, the z score here, z score here is a positive 2. The following questions and answers are from Roger Wimmer's The Research Doctor Archive (with some editing). From the table, ZW=1. If X is a vector, then Z is a vector of z -scores. A Z-score is a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. I'm using a SQL query to determine the z-score (x - μ / σ) of several columns. First move to the left extreme find the value in the z column. This reference group usually consists of people of the same age and gender; sometimes race and weight are also included. 275 is the cumulative area for the negative zvalue and. Enter mean, standard deviation and cutoff points and this calculator will find the area under normal distribution curve. This is because the z score will be in the nonrejection area. Percentile Rank is the easiest score to help you understand how far the attribute measured is above or below the mean of the normative sample. Altman, who was, at the time, an Assistant Professor of Finance at New York University. Helen, one of the volunteers, scored 74 (X) from maximum possible 120 points. P Value from Z Score Calculator. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find. given something called a z-score. See Z-score for more information. 1BestCsharp blog 7,736,621 views. zscores are given along the 1st column and 1st row. Find a critical value in this T value table >>>Click to use a T. The z-score and actual height measurements are both given underscoring the relationship between the two. There are four ways to obtain the values needed for Z α/2:. Detailed information about what a p-value is, how to interpret it, and the difference between one-sided and two-sided tests of sign. What percentage of scores falls below this z score? b. Cardiac Valve Z-Scores Calculate BSA-adjusted z-scores of the mitral valve, tricuspid valve, aortic valve, and pulmonary valve using data published by Cincinnati Children's Hospital. z scores are assumed to have come from a normal population with mean zero and standard deviation one. 8621, As you can see, both values are identical, no matter if you’re using one z score table or another. 8 means it's likely the company is headed for bankruptcy, while companies with scores above 3 are not likely to go bankrupt. The z-score and actual height measurements are both given underscoring the relationship between the two. The most commonly used z-scores are 1. A z-score is a standardized score that describes how many standard deviations an element is from the mean. This online calculator calculates z score from p value. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. 09 at the end of the -1. Anybody’s. Z - score calculator This calculator can be used to find area under standard normal curve  ( \mu=0 , \sigma=1 ). This table identifies the area of the body of the z-distribution. If it is on the right-hand side, we will have a positive value of z else negative. As n approaches 30, the t-score associated with a given confidence level approaches the Z score for that confidence level. To find the value associated with a given z-score, you find the first decimal of your z-score on the left or right side and then the 2nd decimal of your z-score across the top or bottom of the table. Bottom 15% low$$ customers (z-score of the dollar_amt variable less than -1). For example, to determine the area under the curve between 0 and 2. The formula may be used to predict the probability that a firm will go into bankruptcy within two years. The easiest way to find the p-value, though, is to use our p-value calculator! Simply type in the value of the z-score and you will have the p-value calculated in no time!. For negative values just add a "-" sign. The normal random variable X from any normal distribution can be transformed into a z score from a standard normal distribution via the following equation: z = (X - μ) / σ. Since the z-score is a positive number, we look at the Positive Z-Score table for the percent of students who scored within 1. These instructions should allow you to do basic statistical procedures at the level of Math-006 on the TI-83. Above this z score b. 64 : 51st : 0. In statistical inference, we are interested to know whether a small sample comes from a population. 0 versus ZA=4. Let x be any number on our bell curve with mean, denoted by mu, and standard deviation denoted by sigma. In the 5th edition, Table B. Background: In statistics, the z score (also called a z-value, standard score, or normal score) is the signed number of standard deviations by which an observation or data is above the mean. Find the value in a look up table of the probability of a z-score of less than. • A T-score below -2. The formula to calculate z-score is. 4505 in our table [Fig-3]. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find and standard normal tables you need to use. This is one version of a z table. 5 (or 50%) to calculate the area that is to the left of the z score. Next lesson. For any given value of z, this page will calculate the respective one-tailed probabilities of —z and +z; the two-tailed probability of±z; and the proportion of the normal distribution falling between —z and +z. The Z-score or standard deviation classification system. Looking at the table we know P(z <= 3. Detailed information about what a p-value is, how to interpret it, and the difference between one-sided and two-sided tests of significance. So, in this case, it would be 0. This reference group usually consists of people of the same age and gender; sometimes race and weight are also included. However, the calculator below can calculate z score for arbitrary p value. Also Z is one of the common yardsticks for measuring process capability is a Z-score. Use to answer all questions which specify a probability and ask for the relevant range of raw or z-scores. Z score table and calculation z score table t z score table and calculation z score table and calculation Whats people lookup in this blog: Negative Z Score Table Calculator. The z-value calculation is based on algorithm 209 from the CACM by D. As z-value increases, the normal table value also increases. Typically in an introductory stats class, you’d use the z-score and look it up in a table and find the probability that way. There are currently several formulas to compute a z-score. Find a critical value in this T value table >>>Click to use a T. Look at the graph. 32% of students scored lesser than Jack. The Z-score scale is linear and therefore a fixed interval of Z-scores has a fixed height difference in cm, or weight difference in kg, for all children of the same age. 1 Answer to Using the z table in Appendix B, calculate the following percentages for a z score of 0. What is % that is less than 50? I get that I can use a calculator like , or figure out the z-score and then use the z-score table, but is there just a straight calculation where I can plug in the above data and get the right answer (2. Corresponding values which are less than the mean are marked with a negative score in the z-table and respresent the area under the bell curve to theContinue Reading. Z-score calculator, p-value from z-table, left tail, right tail, two tail, formulas, work with steps, step by step calculation, real world and practice problems to learn how to find standard score for any raw value of X in the normal distribution. Above this z score b. A Z score can be determined by multiplying the Ppk score by 3. Coronary Artery Z-Scores. Since the z-score is a positive number, we look at the Positive Z-Score table for the percent of students who scored within 1. The z-score, also known as standard score, is a measurement used in statistics. The area to the left of the negative z-score will be the same as the area to the right of the positive z-score. Use this Z to P calculator to easily convert Z-scores to P-values (one or two-tailed) and see if a result is statistically significant. , z score) that corresponds with Y = 120. Practically speaking, Ppk can be determined by dividing the Z score by three. Z Score Calculator Z Score to Percentile Calculator Left Tailed Test. It is a Normal Distribution with mean 0 and standard deviation 1. The Z-score Calculation. given something called a z-score. Student t-values for both one-tailed (right-tail) and two-tailed probabilities will be returned. Use the following format to find a z-score: z = X - μ / σ. ) Finding the Proportion of Data in a Normal Distribution using the Table ex Find the proportion of data that has z-score less than 0. If NORMSDIST(z) returns p, then NORMSINV(p) returns z. ¨ Using Table A. The whole number and the first digit after the decimal point of the z score is displayed in the row and the second digit in the column of the normal distribution table. The z-score and actual height measurements are both given underscoring the relationship between the two. Finding a corresponding probability is fairly easy. Here’s how to use the table. I have the z-table imported into excel, How i can look-up values from the table to 2 d. 08 and the standard deviation was 3. This wikiHow teaches you how to calculate a Z score in Microsoft Excel. Where they intersect you will find the decimal expression of the percentage of values that are less than your sample (see example 4). With the z-test calculator, users can easily calculate z-score from the p-value or the vice versa. Carry your. Standard normal distribution table is used to find the area under the f(z) function in order to find the probability of a specified range of distribution. Say we need to look up the probability of. 725 is the cumulative area for the positive z. In this case it is 1. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find and standard normal tables you need to use. 64 : 51st : 0. The z-score of 0. Negative Z score table Use the negative Z score table below to find values on the left of the mean as can be seen in the graph alongside. Selecting two-sided provides the area above Z and below -Z. This table identifies the area of the body of the z-distribution. 67 (if our z-score had more than two decimal places, for example, ours was 0. 75 Low Average 87 19 Low Average 86 18 Low Average 85 16 7 400 40 -1. However, it is recommended that you also learn how to make these calculations using either a graphing calculator or Microsoft Excel. Combinations with z Scores. To calculate a Z score, you need to know the mean (μ) and the standard deviation (σ) of your dataset. Using the R score calculator to calculate your R score: Enter the information required in the fields bellow and press the Enter key or on the button "Add class" to calculate the R score for this class. In the following statistical power of negative z score table to explain the how to calculate the probability value For example, P(0 > Z > 2. P Value Calculator Use this calculator to compute a P value from a Z, t, F, r, or chi-square value that you obtain from a program or publication. z scores are assumed to have come from a normal population with mean zero and standard deviation one. 4 indicates that someone is 1.