Question

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50%50% of this population prefers the color red. If 1515 buyers are randomly selected, what is the probability that exactly three-fifths of the buyers would prefer red? Round your answer to four decimal places.

Answer 1

Answer:

0.1527

Step-by-step explanation:

Given that a researcher wishes to conduct a study of the color preferences of new car buyers.

Suppose that 50% of this population prefers the color red

15 buyers are randomly selected

Let X be the no of buyers who prefer red.

X has exactly two outcomes red or non red.

Also each buyer is independent of the other

Hence X is binomial with p = 0.5 and n = 15

Required prob =The probability that exactly three-fifths of the buyers would prefer red

= P(X=9)

= $15C9 (0.9)^9 (0.6)^6$

=$5005(0.0000305)=0.1527$