Question

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 35 employees; the Hawaii plant has 25. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. (Round your answers to four decimal places.)

(a)

What is the probability that none of the employees in the sample work at the plant in Hawaii?

(b)

What is the probability that 1 of the employees in the sample works at the plant in Hawaii?

(c)

What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii?

(d)

What is the probability that 9 of the employees in the sample work at the plant in Texas?

Answer 1

Let X denote the number of employees in the sample works at the plant in Hawaii then X follows a Hypergeometric distribution. The pmf of which is given by:

a) P(none of the employees in the sample work at the plant in Hawaii)=P(X=0) = 0.0024

b) P(1 of the employees in the sample works at the plant in Hawaii) =P(X=1) = 0.0234

c) P(2 or more of the employees in the sample work at the plant in Hawaii) = P(X2) = 1-P(X1) = 0.9742

d) P(9 of the employees in the sample work at the plant in Texas)

= P(1 of the employees in the sample works at the plant in Hawaii) =P(X=1) = 0.0234

Here is the R code I've used for the calculations: