Question

researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population prefers the color red. If 14 14 buyers are randomly selected, what is the probability that exactly 2 2 buyers would prefer red? Round your answer to four decimal places.

Answer 1

Answer: the probability that exactly 2 buyers would prefer red is 0.0320

Step-by-step explanation:

We would assume a binomial distribution for the color preferences of new car buyers. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 14

x = r = 2

Therefore,

P(x = 2) = 14C2 × 0.4^2 × 0.6^(14 - 2)

P(x = 2) = 91 × 0.16 × 0.0022

P(x = 2) = 0.0320