Chapter 5 Exercise Solutions

Chapter 5 Exercise Solutions 

Question 1

The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.

a.    What is the probability that none of the meals will exceed the cost covered by your company (to 4 decimals)?
 

b.    What is the probability that one of the meals will exceed the cost covered by your company (to 4 decimals)?
 

c.     What is the probability that two of the meals will exceed the cost covered by your company (to 4 decimals)?
 

d.    What is the probability that all three of the meals will exceed the cost covered by your company (to 4 decimals)?

Question 2

A university found that 10% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

If you compute the binomial probabilities manually, make sure to carry at least four decimal digits in your calculations.

a.    Compute the probability that 2 or fewer will withdraw (to 4 decimals).
 

b.    Compute the probability that exactly 4 will withdraw (to 4 decimals).
 

c.     Compute the probability that more than 3 will withdraw (to 4 decimals).
 

d.    Compute the expected number of withdrawals.

Question 3

The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). Probability Job Satisfaction Score IS Senior Executives IS Middle Managers 1 .05 .04 2 .09 .10 3 .03 .12 4 .42 .46 5 .41 .28 a.    What is the expected value of the job satisfaction score for senior executives (to 2 decimals)?   b.    What is the expected value of the job satisfaction score for middle managers (to 2 decimals)?   c.     Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals). Executives Middle managers d.      e.    Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives Middle managers f.       g.    What comparison can you make about the job satisfaction of senior executives and middle managers? Select Senior executives have higher satisfaction with more variation Senior executives have higher satisfaction with less variation Middle managers have higher satisfaction with more variation Middle managers have higher satisfaction with less variation Item 7

Question 4

Consider a binomial experiment with n = 20 and p = .70. If you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. a.    Compute f(12) (to 4 decimals).   b.    Compute f(16) (to 4 decimals).   c.     Compute P(x  16) (to 4 decimals).   d.    Compute P(x  15) (to 4 decimals).   e.    Compute E(x).   f.     Compute Var(x) (to 1 decimal) and  (to 2 decimals). Var(x)

Question 5

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.

a.    What is the expected number of calls in one hour?
 

b.    What is the probability of three calls in five minutes (to 4 decimals)?
 

c.     What is the probability of no calls in a five-minute period (to 4 decimals)?

Question 6

The following table provides a probability distribution for the random variable x.

	x	f(x)
	3	.25
	6	.50
	9	.25

a.    Compute E(x), the expected value of x.
 

b.    Compute ², the variance of x (to 1 decimal).
 

c.     Compute , the standard deviation of x (to 2 decimals).