1. Before doing this assignment, do the practice problem posted under Apply and Discover.

2. Word-process your solutions within this template. Do not create a new file.

3. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.

4. Word-process formulas using Equation Editor and diagrams using Drawing Tool.

Problem 1

If many 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 would be the mean, variance, standard deviation 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, each sample consists of 100 items) were taken from a large non-normal population with a mean of 10 and variance of 16, what would be the mean, variance, standard deviation 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 3

Time lost due to employee absenteeism is an important problem for many companies. The human resources department of Western Electronics has studied the distribution of time lost due to absenteeism by individual employees. During 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 probability that the number of absences for this one employee would exceed 25 days?

b) If many samples of 36 employees each are taken and sample means computed, a distribution of sample means would result. What would be the mean, standard deviation and shape of the distribution of sample means for samples of size 36? Give reasons for your answers.

c) A group of 36 employees is selected at random to participate in a program that allows a flexible work schedule, which the human resources department hopes will decrease the employee absenteeism in the future. What is the probability that the mean for the sample of 36 employees randomly 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