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

Answer:

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

Step-by-step 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

    $P(X = 5) = 792 * (0.45)^5 * (0.45)^{12- 5 }$

    $P(X = 5) = 0.222$