Question

Five percent of American truck drivers are women (Statistical Abstract of the United States, 1997). Suppose 10 truck drivers are selected randomly to be interviewed about quality of work conditions. This is a binomial distribution. (Use Minitab. Print out the Minitab worksheet results and include a picture of that sheet at the end of the test.)

a. What is the probability that exactly two of the drivers will be women?

b. What is the probability that none will be women?

c. What is the probability that at least one will be a women?

d. What is the probability that more than 2 will be a women?

Answer 1

a)

from Minitab: go to Calc: Probability distribution: binomial: probility: number of trails : 10 , event probability =0.05 ,Input constant : 2

below is output:

Probability Density Function

Binomial with n = 10 and p = 0.05

x P( X = x )
2   0.0746348

b)

Probability Density Function

Binomial with n = 10 and p = 0.05

x P( X = x )
0    0.598737

c)

Cumulative Distribution Function

Binomial with n = 10 and p = 0.05

x P( X ≤ x )
1    0.913862

therefore P(X>=2 )=1-P(X<=1) =1- 0.913862 =0.086138

d)

Cumulative Distribution Function

Binomial with n = 10 and p = 0.05

x P( X ≤ x )
2    0.988496

therefore P(X>2 )=1-P(X<=2) =1- 0.988496=0.011504