Axline Computers manufactures personal computers at two plants, one in Texas and

Question

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. 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?

Explanation / Answer

Solution:-

Number of employees in Texas = 40

Number of employees in Hawai = 20

Total number of employees = 60

Probability of employees in Texas = 40/60 = 0.667

Probability of employees in Hawaii = 20/60 = 0.3333

a) The probability that none of the employee in sample work at hawaii plant is 0.01734.

p = 0.3333, n = 10, x = 0

By applying binomial distribution:-

P(x, n, p) = nCx* px *(1 - p)(n - x)

P(x = 0) = 0.0174

b) The probability that one of the employee in sample work at hawaii plant is 0.0867.

p = 0.3333, n = 10, x = 1

By applying binomial distribution:-

P(x, n, p) = nCx* px *(1 - p)(n - x)

P(x = 1) = 0.0867

c) The probability that 2 or more of the employee in sample work at hawaii plant is 0.8959.

p = 0.3333, n = 10, x = 2

By applying binomial distribution:-

P(x, n, p) = nCx* px *(1 - p)(n - x)

P(x > 2) = 0.8959

d) The probability that 9 of the employee in sample work at Texas plant is 0.0867.

p = 0.6667, n = 10, x = 9

By applying binomial distribution:-

P(x, n, p) = nCx* px *(1 - p)(n - x)

P(x = 9) = 0.0867

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