Question

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green

Answer 1

The probability that exactly 12 buyers would prefer green

=0.00555

Explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

`P(X=x)=nC_r p^r q^(n-r)`

`P(x=12)=14C_(12)(0.50)^(12)(0.50)^(14-12)`

`P(x=12)=14C_(12)(0.50)^(12)(0.50)^2`

`P(x=12)=14C_(12)(0.50)^(14)`

`P(x=12)=(14!)/(12!2!)(0.50)^(14)`

`P(x=12)=(14* 13* 12!)/(12!2* 1)(0.50)^(14)`

`P(x=12)=91\cdot (0.50)^(14)`

`P(x=12)=0.00555`

Hence, the probability that exactly 12 buyers would prefer green

=0.00555