Assignment 05

Assignment05

1. Compute the mean and variance of the following discreteprobability distribution.

X

P(x)

X*p(x)

X^2*P(x)

2

.50

1

2

8

.30

2.4

19.2

10

.20

2

20

total

5.4

41.2

The mean is given by

Mean = sum(X*p(x))

= 1+2.4+2

= 5.4

the variance = sum (X2*P(x))– (sum(X*p(x)))2

=41.2– 5.42

=12.04

2. The Computer Systems Department has eight faculty, six of whom aretenured. Dr. Vonder, the chair, wants to establish a committee ofthree department faculty members to review the curriculum. If sheselects the committee at random:

a. What is the probability all members of the committee are tenured?

Probability that all are tenured is equal to probability they are allfrom those tenured

= probability of selecting a tenured department is 

Hence probability that the tree department are form the 

b. What is the probability that at least one member is not tenured?(Hint: For this question, use the complement rule).

probability that at least one member is not tenured i= 1 –probability that all are tenured

3. New Process, Inc., a large mail-order supplier of women’sfashions, advertises same-day service on every order. Recently, themovement of orders has not gone as planned, and there were a largenumber of complaints. Bud Owens, director of customer service, hascompletely redone the method of order handling. The goal is to havefewer than five unfilled orders on hand at the end of 95% of theworking days. Frequent checks of the unfilled orders follow a Poissondistribution with a mean of two orders. A Poisson distribution is adiscrete frequency distribution.

Has New Process, Inc. lived up to its internal goal? Cite evidence.

4. Recent information published by the U.S. Environmental ProtectionAgency indicates that Honda is the manufacturer of four of the topnine vehicles in terms of fuel economy.

a. Determine the probability distribution for the number of Hondas ina sample of three cars chosen from the top nine.

Let x be the number of Honda selected. The probability distributionof the number of Hondas in a sample of three cars chosen from the topnine is

f(x) = , x = 0,1,2,3,4,5,……

  1. elsewhere

b. What is the likelihood that in the sample of three at least oneHonda is included?

The likelihood that in the sample of three at least one Honda isincluded is