It is known that the length of a certain product X is normally distributed with μ = 20 inches and σ = 4 inches. How is the probability P(X 28) related to P(X 28) is greater than (X 28) is smaller than (X 28) 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 and σ = 4 inches. How is the probability P(X > 28) related to P(X < 16)? A) P(X > 28) is greater than (X < 16). B) P(X > 28) is smaller than (X < 16). C) P(X > 28) is the same as P(X < 16). D) No comparison can be made with the given information.

Quizplus · Accepted Answer

We know that the length of the product X is normally distributed with μ = 20 inches and σ = 4 inches. To find P(X > 28), we can standardize the variable X using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean and σ is the standard deviation. z = (28 - 20) / 4 = 2 We can now use a standard normal table or calculator to find the probability P(Z > 2) = 0.0228. To find P(X < 16), we can standardize the variable X as before: z = (16 - 20) / 4 = -1 Using the same standard normal table or calculator, we can find P(Z < -1) = 0.1587. Therefore, we can see that P(X > 28) is smaller than P(X < 16), which means choice B is the correct answer.

It Is Known That the Length of a Certain Product