Question

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 60% of this population prefers the color black. If 16 buyers are randomly selected, what is the probability that exactly 3 buyers would prefer black? Round your answer to four decimal places.

A) 0.0873
B) 0.2240
C) 0.3686
D) 0.5546

Answer 1

If a researcher wishes to conduct a study of the color preferences of new car buyers. The probability that exactly 3 buyers would prefer black is:

B) 0.2240.

What is the probability?

Using the binomial probability formula

The formula for the probability of exactly x successes in n trials given a probability p of success in a single trial is:

`P(X = x) = (nCx) * p^x * (1-p)^(n-x)`

Plugging the values into the formula:

`P(X = 3) = (16C3) * (0.6)^3 * (1-0.6)^(16-3)`

`P(X = 3) = 0.2240`

The probability that exactly 3 buyers would prefer black is approximately 0.2240.

Therefore the correct option is B) 0.2240.