Sample problems for chapter 5
7, p. 216
The probability distribution for the random variable x follows.
x f(x)
20 .20
25 .15
30 .25
35 .40
a. Is this probability distribution valid? Explain
b. What is the probability that x = 30?
c. What is the probability that x is less than or equal to 25?
d. What is the probability that x is greater than 30?
21, p. 223
The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
Probability
Job IS Senior IS Middle
Satis. Executives Managers
Score f(x) xf(x) (x – μ) (x – μ)2 (x – μ)2f(x) f(x) xf(x) (x – μ) (x – μ)2 (x – μ)2f(x)
1 .05 .05 -3.05 9.3025 .465 .04 .04 -2.84 8.0656 .323
2 .09 .18 -2.05 4.2025 .378 .10 .20 -1.84 3.3856 .339
3 .03 .09 -1.05 1.1025 .033 .12 .36 -.84 .7056 .085
4 .42 1.68 -.05 .0025 .001 .46 1.84 .16 .0256 .012
5 .41 2.05 .95 .9025 .370 .28 1.40 1.16 1.3456 .377
Σ = 4.05 1.247 3.84 1.136
SD 1.117 1.066
a. What is the expected value of the job satisfaction score for senior executives?
b. What is the expected value of the job satisfaction score for middle managers?
c. Compute the variance of job satisfaction scores for executives and middle managers.
d. Compute the standard deviation of job satisfaction scores for both probability distributions.
e. Compare the overall job satisfaction of senior executives and middle managers.
33, p. 235
Twelve of the top twenty finishers in the 2009 PGA Championship at Hazeltine National Golf Club in Chaska, Minnesota, used a Titleist brand golf ball (GolfBallTest website, November 12, 2009). Suppose these results are representative of the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball. For a sample of 15 PGA Tour players, make the following calculations.
a. Compute the probability that exactly 10 of the 15 PGA Tour players use a Titleist brand golf ball.
b. Compute the probability that more than 10 of the 15 PGA Tour players use a Titleist brand golf ball.
c. For a sample of 15 PGA Tour players, compute the expected number of players who use a Titleist brand golf ball.
d. For a sample of 15 PGA Tour players, compute the variance and standard deviation of the number of players who use a Titleist brand golf ball.
43, p. 241
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute.
a. Compute the probability of no arrivals in a one-minute period.
b. Compute the probability that three or fewer passengers arrive in a one-minute period.
c. Compute the probability of no arrivals in a 15-second period.
d. Compute the probability of at least one arrival in a 15-second period.
55, p. 248
The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2.
a. Show the probability distribution for the expense forecast.
b. What is the expected value of the expense forecast for the coming year?
c. What is the variance of the expense forecast for the coming year?
d. If income projections for the year are estimated at $12 million, comment on the financial position of the college.