Question

Suppose that 20.3% of car engines will fail if they have not had routine maintenance in the past five years. if routine maintenance is given to 26 cars, what is the probability that exactly 14 will not have engine failure? round your answer to six decimal places.

Answer 1

The probability that exactly 14 out of 26 cars will not have engine failure is approximately 0.185429.

Step-by-step explanation:

To find the probability that exactly 14 out of 26 cars will not have engine failure, we can use the binomial probability formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of success, and p is the probability of success.

In this case, n = 26, k = 14, and p = 0.797. Plugging the values into the formula, we get:

P(X=14) = (26 choose 14) * (0.797)^14 * (1-0.797)^(26-14)

Calculating this expression, we find that the probability is approximately 0.185429.