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 16 buyers are randomly selected, what is the probability that exactly 7 buyers would prefer green? round your answer to four decimal places.

We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p) ˣ (1-p) ⁿ-ˣ

We have

n, the number of trial = 16

x, the sample we aim to try = 7

p, the probability of success = 0.5

Substitute these values into the formula

P (7) = ¹⁶C₇ (0.5) ⁷ (1-0.5) ¹⁶⁻⁷

P (7) = 0.1746 (rounded to four decimal places)