Question

Industry standards suggest that 9% of new vehicles require warranty service within the first year. bauer nissan in sumter, south carolina, sold 12 nissans yesterday.

what is the probability that none of these vehicles requires warranty service? note: round your answer to 4 decimal places.
what is the probability exactly one of these vehicles requires warranty service?

Answer 1

To calculate the probability that none of the 12 vehicles sold by Bauer Nissan requires warranty service, we use the binomial probability formula with p=0.09 and n=12 and find it to be approximately 0.3138. For exactly one vehicle requiring service, the probability is approximately 0.3762.

Step-by-step explanation:

The probability that none of the 12 vehicles sold by Bauer Nissan require warranty service can be calculated using a binomial probability formula where the success probability (p) is the chance that a car requires warranty service (9%) and the number of trials (n) is the number of cars sold (12). The probability of success on any given trial is 0.09, and we are interested in the probability of zero successes (no cars requiring warranty service).

The formula for the probability of k successes in n trials is given by:
P(X = k) = C(n, k) * (p^k) * (1 - p)^(n - k)

Where C(n, k) is the combination of n items taken k at a time. For the case of zero cars requiring warranty service (k = 0):

To find the probability that exactly one of these vehicles requires warranty service, we set k = 1: