Answer:
The probability is [tex]P(X = 5) = 0.222[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of business travelers that plan their own business trip is [tex]p = 0.45[/tex]
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
[tex]q = 1- p[/tex]
=> [tex]q = 1-0.45[/tex]
=> [tex]q = 0.55[/tex]
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
[tex]P(X = 5) = ^{12} C_5 * p^5 * q^{12- 5 }[/tex]
Generally using a combination calculator
[tex]^{12} C_5 = 792[/tex]
So
[tex]P(X = 5) = 792 * (0.45)^5 * (0.45)^{12- 5 }[/tex]
[tex]P(X = 5) = 0.222[/tex]
