4.The number of electrical outages in a town varies from day to day. Assume that this daily number has the following probability distribution.

x	f(x)
0	0.80
1	0.15
2	0.04
3	0.01

The mean and the standard deviation for the daily number of electrical outages (respectively) are

a.	2.6 and 5.77
b.	0.26 and 0.577
c.	3 and 0.01
d.	0 and 0.8

ANS:B

5.Which of the following is not a property of a binomial experiment?

a.	The experiment consists of a sequence of n identical trials
b.	For each trial, there are two possible outcomes called success and failure
c.	the probabilities of getting success and failure can change from one trial to the next
d.	the trials are independent

ANS:C

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6.A probability distribution showing the probability of x successes in n independent trials, where the probability of success does not change from trial to trial, is termed a

a.	uniform probability distribution
b.	binomial probability distribution
c.	hyper-geometric probability distribution
d.	normal probability distribution

ANS:B

7.The mean and the standard deviation of a binomial distribution are

a.	and
b.	and = np
c.	= np and = np(1 - p)
d.	None of these alternatives is correct

ANS:D

8.40% of Chicago workers use public transportation daily. For a sample of 50 workers, what is the expected value and the variance of the number of workers who use public transportation daily.

a.	20 workers and 3.46 workers, respectively
b.	20 workers and 12 (worker)2, respectively
c.	12 workers and 20 (worker)2, respectively
d.	40 workers and 50 workers, respectively

ANS:B

9.Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a.	0.2592
b.	0.0142
c.	0.9588
d.	0.7408

ANS:B

Exhibit 5-1

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.

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10.Refer to Exhibit 5-1. What is the expected number of female students in the sample?

a.	6.0
b.	4.8
c.	3.2
d.	8.0

ANS:B

11.Refer to Exhibit 5-1. What is the standard deviation of the number of female students in the sample?

a.	1.386
b.	1.920
c.	4.804
d.	6.085

ANS:A

12.Refer to Exhibit 5-1. What is the probability that among the 8 students exactly two are female?

a.	0.0896
b.	0.2936
c.	0.0413
d.	0.0007

ANS:C

13.Refer to Exhibit 5-1. What is the probability that among the 8 students at least 7 are female?

a.	0.1064
b.	0.0896
c.	0.0168
d.	0.8936

ANS:A

14.Refer to Exhibit 5-1. What is the probability that among the 8 students at least 6 are male?

a.	0.0413
b.	0.0079
c.	0.0007
d.	0.0499

ANS:D

PROBLEMS

A financial analyst has constructed the following probability distribution for a firm predicted percent return for the upcoming year.

Return x

Probability f(x)

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-5%	0.20
0%	0.30
5%	0.40
10%	0.10

What is the expected value of the return?

What is the standard deviation of the return?

ANS:

= 2, that is, 2%

The variance is 2 = 21, that is 21(%)2. So, the standard deviation is , that is, 4.58%.

5-2.The demand for a product varies from month to month. Based on the past year's data, the following probability distribution describes the monthly demand for a product.

x	f(x)
Unit Demand	Probability
0	0.10
1,000	0.10
2,000	0.30
3,000	0.40
4,000	0.10

a.	Determine the expected number of units demanded per month.
b.	Each unit produced costs the company $8, and is sold for $10. How much will the company gain or lose in a month if they produce the expected number of units demanded, but sell 2000 units?

ANS:

a.	2300
b.	Profit = 2000($10) 2300($8) = $1600

5-3.Seventy percent of the students applying to a university are accepted. Eighteen applications are now under review.

a.	What is the probability that exactly 10 will be accepted?
b.	What is the probability that exactly 5 will be rejected?
c.	What is the probability that at least 7 will be accepted?
d.	What is the probability that more than 15 will be accepted?
e.	What is the expected number of the accepted applications?
f.	What is the standard deviation of the number of accepted applications?

ANS:

a.	0.0811
b.	0.2017

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c.	0.9986
d.	0.06
e.	12.6
f.	1.9442