Question

Five percent of the 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.

Explain why the selection of the 10 drivers is a binomial experiment.

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

What is the probability that none will be women?

What is the probability that at least one will be woman?

Answer 1

a)

Selection of 10 drivers is binomial experiment because,

i) Number of observations are fixed.

ii) Selection of trials is independent and random.

iii) Probability is fixed fo all trials.

b)

X ~ Binomial (n,p) = Binomial(10,0.05)

P(X = x) = ⁿC_x p^x (1-p)^n-x

P(X = 2) = ¹⁰C₂ 0.05² 0.95⁸

= 0.0746

Probability that two of the drivers are women = 0.0746

c)

P( X = 0) = ¹⁰C₀ 0.05⁰ 0.95¹⁰

= 0.5987

Probability that none of the drivers are women = 0.5987

d)

P(X >=1) 1 - P( X = 0)

= 1 - 0.5987

= 0.4013

Probability that at least one drivers will be women = 0.4013