Question

1. The Math department at CBC has 14 full-time faculty. Four of them received degrees from WSU. If a committee of three is randomly chosen among the department members, what is the probability that no one on the committee has a degree from WSU?

a) .011

b) .670

c) .330

D) .099

2. In 2018, only 2% of new cars solds had a manual transmission. If five new cars are selected at random from those sold in 2018, find the probability that exactly one of them had a manual transmission.

a) 0.02

b) 0.98

c) 0.092

d) 0.018

e)0.00000078

Answer 1

Q.1) This is a direct application of Hypergeometric distribution.

Where, population size (N) = 14, success in population = k = 4

number of sample (n) = 3 and number of success in samples = x = 0

We want to find, P(X = 0)

Using Excel we find this probability as follows:

Excel Command : ==HYPGEOMDIST(0,3,4,14) = 0.330

=> P(X = 0) = 0.330

Answer : c) 0.330

Q 2) This is a direct application of Binomial distribution,

where, n = 5 and p = 0.02

X ~ Binomial (n = 5, p = 0.02)

We want to find, P(X = 1)

=> P(X = 1) = 0.092

Excel Command : =BINOMDIST (1, 5, 0.02, 0) = 0.092

Answer : c) 0.092