Problem 1

If various samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what could be the mean, standard deviation, variance, and shape of the distribution of sample means? Give reasons for your answers.

Note: Variance is the square of the standard deviation.

Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon. 1993

Problem 2

If many samples of size 100 (that is, every sample consists of 100 items) were taken from a large non-normal population with a mean of 10 and variance of 16, what could be the mean, variance, standard deviation and shape of the distribution of sample means? Provide reasons for your answers.

Note: Variance is the square of the standard deviation.

Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon. 1993

Problem 3

Time lost because of employee absenteeism is an important problem for various companies. The human resources department of Western Electronics has studied the allocation of time lost due to absenteeism by individual employees. Through a one-year period, the department found a mean of 21 days and a standard deviation of 10 days based on data for all the employees.

a) If you pick an employee at random, what is the possibility that the number of absences for this one employee would exceed 25 days?

b) If various samples of 36 employees each are taken and sample means computed, a distribution of sample means could result. What could be the mean, standard shape and deviation of the distribution of sample means for samples of size 36?

c) A group of 36 employees is chosen at random to participate in a program that allows a flexible work schedule, which the human resources department hopes may decrease, the employee absenteeism in the future. What is the possibility that the mean for the sample of 36 employees arbitrarily selected for the study would exceed 25 days?

Source: Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Chapter 7 Page 305. Fifth Edition. Allyn and Bacon. 1993

Problem 4

The amount of time a bank teller spends with each customer has a population mean x = 3.1 minutes and population standard deviation x = 0.4 minute.

a) What is the possibility that for a arbitrarily selected customer the service time could exceed 3 minutes?

b) If various samples of 64 were selected, what are standard and mean error of the mean (standard deviation of sample means) expected to be? What is expected to be the shape of the distribution of sample means?

c) If a random sample of 64 customers is selected, determine the probability that the sample mean would exceed 3 minutes?

Source: Statistics for Business and Economics by Berenson and Levine. Second Edition. Chapter 9 Page 318. Ally and Bacon. 1993