Question

Given a Normally distributed population with a mean of 175 and astandard deviation of 40, find x such that Pr(X > x) = 0.475.(Please round your answer to one decimal place, e.g. 0.6.)

Answer 1

To find x such that Pr(X > x) = 0.475, you can use the Z-score formula. In this case, x is approximately 257.4.

Step-by-step explanation:

To find x such that Pr(X > x) = 0.475, we need to use the Z-score formula. The Z-score formula is: Z = (X - μ) / σ, where Z is the standard score, X is the value we're looking for, μ is the mean, and σ is the standard deviation. In this case, we have μ = 175, σ = 40, and we want to find x such that the probability that X is greater than x is 0.475.

First, we need to find the Z-score corresponding to a probability of 0.475. The Z-score table gives us the value 1.96. Now we can rearrange the formula to solve for X: x = Z * σ + μ. Substituting the values, we get x = 1.96 * 40 + 175 = 257.4. Therefore, x is approximately 257.4.