Statistical Analysis

Calculate the mean and variance of the discrete probability distribution shown below. xP(x) 2.508.3010.20

Solution

Mean = (2*0.5) + (8*0.3) + (10*0.2) = 5.4

Variance = d2*P(x), where d is x's deviation from the mean.

Variance = (8-5.4)20.3 + (2-5.4)2*0.5 (10-5.4)

2*0.2 = 12.04

Question No. 2

The Computer Systems Department includes eight tenured faculty members. The chair, Dr. Vonder, wishes to form a committee of three department faculty members to assess the curriculum. If she chooses the committee at random, what is the likelihood that all members will be tenured? Solution

The probability of selecting 3 tenured members = 6/8 x 5/7 x 4/6 = 5/14 or 0.3571

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

This is the same as the probability as either one member is not tenured or the two members are not tenured.

Probability = 1/8 + 2/8 = 3/8

Question 3New Process, Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95% of the working days. Frequent checks of the unfilled orders follow a Poisson distribution with a mean of two orders. A Poisson distribution is a discrete frequency distribution.Has New Process, Inc. lived up to its internal goal? Cite evidence.

Solution

P(k