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

Quizplus · Accepted Answer

Since μ = 20 inches is the mean of the normal distribution, P(X < 20) represents the probability of a length less than the mean, which is 0.5 or 50%. P(X < 16) would represent a value further left on the distribution curve, thus having a smaller probability than P(X < 20).

It Is Known That the Length of a Certain Product