A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, what value will 15% of the observations be below?
A) 19.8
B) 16.2
C) 18.7
D) 17.2

Question

Quizplus · Accepted Answer

To find the value below which 15% of the observations fall, we need to find the z-score that corresponds to the 15th percentile. Using a standard normal distribution table or calculator, the z-score for 0.15 is approximately -1.04. Using the formula X = μ + zσ, where μ = 25 and σ = 5, we get X = 25 + (-1.04)(5) = 19.8.

A Random Variable Is Normally Distributed with a Mean of 25