Question

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.

Answer 1

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)