# The Normal Distribution Worksheet

Posted: March 2nd, 2021

1.Social scientists discovered that 1013 General Social Survey (GSS) respondents in 2010 watched television for an average of 3.01 hours per day with a standard deviation of 2.65 hours per day. Answer the following questions assuming the distribution of the number of television hours is normal. QUESTION 2

2. Information on the occupational prestige scores for blacks and whites is presented in the following table. Mean Standard Deviation N Whites 45.03 13.93 1100 Blacks 40.83 13.07 195 Source: GSS 2010. 1

QUESTION 3 a. If you have 13.47 years of education that is the mean number of years of education what is your Z score? ____ QUESTION 4

QUESTION 5 1.The mean age at first marriage for respondents in a survey is 23.33 with a standard deviation of 6.13. Calculate the observed age at first marriage associated with a Z score of -0.72. 1.The mean age at first marriage for respondents in a survey is 23.33 with a standard deviation of 6.13. The Z score associated with a particular age at first marriage is 0.35. If the proportion of the area between this particular age at first marriage and the mean is 0.14 what proportion of respondents experienced their first marriage earlier than this age? Hint: Draw the picture. You do not need to use the table. 1.The mean age at first marriage for respondents in a survey is 23.33 with a standard deviation of 6.13. Suppose that a person experienced their first marriage at age 23. If the area beyond the Z score associated with age 23 is 0.24 what proportion of respondents experienced their first marriage before age 23? Hint: Draw the picture. You do not need to use the table. 1.The mean age at first marriage for respondents in a survey is 23.33 with a standard deviation of 6.13. Suppose that a person experienced their first marriage at age 23. If the area beyond the z-score associated with age 23 is 0.24 what proportion of respondents experienced their first marriage after age 23? Hint: Draw the picture. You do not need to use the table. 1.When the Scholastic Aptitude Test (SAT) – now known as the Scholastic Assessment Test – was first developed the idea was that each section of the test would have a mean of 500 and a standard deviation of 100. While the SAT is continually adjusted and readjusted to promote such a distribution lets assume for this exercise that math scores on the SAT have a mean of 500 and a standard deviation of 100. 1.Suppose that a student receives a 465 on the math section of the SAT. What is the z-score that corresponds to this raw score? 2.What percentage of students who took the SAT scored below 465? 3.What percentage of students who took the SAT scored below 465? 4.What percentage of students who took the SAT scored between a 465 and 500? What is the Z score for a person who watches more than 8 hours per day? _______________________________ What proportion of people watch television less than 5 hours per day? __________________________________ How many people does this correspond to in the sample? ____________________________________________ What number of television hours per day corresponds to a Z score of +1? ________________________________ What is the percentage of people who watch between 1 and 6 hours of television per day? _________________ What percentage of whites should have occupational prestige scores above 60? __________________________ How many whites in the sample should have occupational prestige scores above 60? ______________________ What percentage of blacks should have occupational prestige scores above 60? __________________________ How many blacks in the sample should have occupational prestige scores above 60? _______________________ What proportion of whites have prestige scores between 30 and 70? ___________________________________ How many whites have prestige scores between 30 and 70? __________________________________________ How many blacks in the sample should have occupational prestige scores between 30 and 60? ______________ Let’s assume that education is normally distributed. Using GSS data we find the mean number of years of education is 13.47 with a standard deviation of 3.1. A total of 1496 respondents were included in the survey. Use these numbers to answer the following questions. The 2007 Law Enforcement and Management Statistics (LEMAS) survey reported that the mean number of municipal police per 1000 citizens in U.S. cities with populations of 100000 or more was 1.99 (s = 0.84). One department had 4.28 police per 1000 residents. Convert this raw score to a z score: ___________________________________________________________ Find the area between the mean and z. _________________________________________________________ Find the area in the tail of the distribution beyond z. _______________________________________________ ‘

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