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

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step 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

$P(X=x)=nC_r p^r q^{n-r}$

$P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}$

$P(x=12)=14C_{12}(0.50)^{12}(0.50)^2$

$P(x=12)=14C_{12}(0.50)^{14}$

$P(x=12)=\frac{14!}{12!2!}(0.50)^{14}$

$P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}$

$P(x=12)=91\cdot (0.50)^{14}$

$P(x=12)=0.00555$

Hence, the probability that exactly 12 buyers would prefer green

=0.00555