08 Jul Principles of Business Statistics
Principles of Business Statistics
Problem Set # 4
Due Thursday March 9th in Class
(Covers chapter 7)
Round off all numerical answers to two decimal places.
1. A report finds that the population mean television viewing time for Americans is 15
hours per week. The report also finds the population variance to be 16 hours per week.
A sample of 60 Americans is taken to further investigate television viewing habits.
(6 Points)
a. Graph the sampling distribution of x , that is graph the sampling distribution curve for the sample mean of 60 American television viewing times. On the graph make
sure to indicate μ and report the standard error of the mean.
b. What is the probability the sample mean will be within 45 minutes of the population mean?
2. A population is normally distributed with a population standard deviation of 49.
Compute the standard error of the mean for sample sizes of 50, 100 and 200. What can
you say about the size of the standard error of the mean as the sample size is increased?
(4 Points)
3. The College Board American Testing Program reported (population) mean SAT score of
920 and a population standard deviation of 130. (5 Points)
a. What is the standard error of the mean for a random sample of 100 students’ SAT scores?
b. How many students must be sampled to decrease the standard error of the mean to 1? c. What is the probability that a random sample of 75 students will provide a sample
mean SAT score within 10 (i.e. ± 10) of the population mean?
d. What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 (i.e. ± 20) of the population mean?
e. What is the probability that a random sample of 100 students will provide a sample mean less than an SAT score of 950?
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