It is estimated that 20% of luxury cars manufactured in 2008 were silver.A car dealership typically sells 20 luxury cars per month.The probability that 8 of the luxury
Cars sold per month are silver is
A).0006.
B).1276.
C).0222.
D).7779
E)None of the above.

Question

Quizplus · Accepted Answer

The problem involves a binomial distribution, where we have a fixed number of trials (i.e. the number of luxury cars sold per month) and each trial has only two possible outcomes (i.e. silver or not silver). We are given that the probability of a luxury car being silver is 0.2.

We want to find the probability of 8 out of 20 luxury cars sold in a month being silver. Using the binomial distribution formula, we have:

P(X = 8) = (20 choose 8) * (0.2)^8 * (0.8)^12

where (20 choose 8) is the number of ways to choose 8 silver cars out of 20 (i.e. a combination). Using a calculator, we find:

(20 choose 8) = 125970

Plugging this and the given probabilities into the formula, we get:

P(X = 8) = 125970 * (0.2)^8 * (0.8)^12

P(X = 8) ≈ 0.0222

So the probability that 8 luxury cars sold in a month are silver is approximately 0.0222, or choice C.

It Is Estimated That 20% of Luxury Cars Manufactured in 2008