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 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green? Round your answer to four decimal places.

Answer 1

Solution:

Let X be a random variable which represents the number of car buyers who prefer green color.

50% of the population prefers the color green.

Hence, probability that a car buyer would prefer green color is 50/100 = 0.50.

Let's consider the car buyers who prefer green color as success. Hence, now we have only two outcomes one is success and other is failure.

Probability of success (p) = 0.50

Number of trials (n) = 14

Since, we have only two mutually outcomes (success and failure), number of trials (n) is finite and probability of success remains constant in every trial, therefore we can consider that X is binomial distributed random variable.

According to binomial probability law, probability of occurrence of exactly x successes in n trials is given by,

We have to obtain P(X = 12).

we have, p = 0.50 and n = 14

The probability that exactly 12 buyers would prefer green color is 0.0056.

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