Question

1. A recent study revealed that 45% of business travelers plan their own business trips. The study is to be replicated with a sample of 12 frequent business travels. a. What is the probability exactly 5 travelers plan their own trips

Answer 1

The probability is
`P(X = 5) = 0.222`

Explanation:

From the question we are told that

The proportion of business travelers that plan their own business trip is
`p = 0.45`

The sample size is n = 12

The random number considered is x = 5

Generally the proportion of business travelers that do not plan their own business trip is mathematically evaluated as

`q = 1- p`

=>
`q = 1-0.45`

=>
`q = 0.55`

This can study can be said to follow binomial distribution as there is only two outcomes

So the probability exactly 5 travelers plan their own trips is mathematically represented as

`P(X = 5) = ^(12) C_5 * p^5 * q^(12- 5 )`

Generally using a combination calculator

`^(12) C_5 = 792`

So

`P(X = 5) = 792 * (0.45)^5 * (0.45)^(12- 5 )`

`P(X = 5) = 0.222`