A random variable X is normally distributed with mean 100 and standard deviation 20. Below what value of X does 25% of the probability lie?
A) 83
B) 85
C) 87
D) 89
E) 90

Question

Quizplus · Accepted Answer

The 25th percentile of a normal distribution corresponds to a Z-score of approximately -0.675. Using the formula X = μ + Zσ, where μ is the mean and σ is the standard deviation, we can calculate the value of X. Plugging in the values: X = 100 + (-0.675)(20) = 100 - 13.5 = 86.5. The closest value to 86.5 among the options is 87.

A Random Variable X Is Normally Distributed with Mean 100