A random variable is normally distributed with a mean of -50 and a standard deviation of 10. If an observation is randomly selected from the distribution, what value will be exceeded 10% of the time?
A) -37.20
B) -62.80
C) 62.80
D) 37.20

Question

Quizplus · Accepted Answer

The value that will be exceeded 10% of the time corresponds to the 90th percentile of the distribution. Using the Z-score formula and looking up the Z-score for the 90th percentile (which is approximately 1.28), we can calculate the corresponding value in the distribution. The formula is X = μ + Zσ, where μ is the mean, Z is the Z-score, and σ is the standard deviation. Plugging in the values: X = -50 + (1.28)(10) = -50 + 12.8 = -37.20.

A Random Variable Is Normally Distributed with a Mean of -50