Question

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color brown. If 18 buyers are randomly selected, what is the probability that exactly a third of the buyers would prefer brown? Round your answer to four decimal places.

Answer 1

0.1655

Explanation:

Answer 2

0.1655

Explanation:

This is a binomial probability.

THe formula is:

`nCr*p^r*(1-p)^(n-r)`

Where n is the total number of people

r is how many we want (we want 1/3rd of 18 which is 6, r= 6)

p is probability of success (0.4)

Putting the information, we get:

`nCr*p^r*(1-p)^(n-r)\\=18C6*(0.4)^(6)(0.6)^(12)\\=0.1655`

Thus, the probability that exactly a third of the buyers would prefer brown is 0.1655