A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color brown. If 18 buyers are randomly selected, what is the probability that exactly 8 buyers would prefer brown? Round your answer to four decimal places.

0.0811 is the probability that exactly 8 buyers would prefer brown.

Step-by-step explanation:

We are given the following information:

We treat people preferring color brown as a success.

P(prefer color brown) = 30% = 0.30

Then the number of buyers follows a binomial distribution, where

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 18

We have to evaluate:

0.0811 is the probability that exactly 8 buyers would prefer brown.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are