It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X 24) related to P(X 24) is greater than P(X 24) is smaller than P(X 24) is the same as P(X

Question

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 24) related to P(X < 16)? A) P(X > 24) is greater than P(X < 16). B) P(X > 24) is smaller than P(X < 16). C) P(X > 24) is the same as P(X < 16). D) No comparison can be made with the given information.

Quizplus · Accepted Answer

Since the normal distribution is symmetric around the mean, the probability of a value being more than 4 inches above the mean (μ + 4 = 24) is the same as the probability of a value being more than 4 inches below the mean (μ - 4 = 16). Therefore, P(X > 24) is the same as P(X < 16).

It Is Known That the Length of a Certain Product