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, determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.
A) 18.85 and 27.94
B) 19.31 and 21.12
C) 16.23 and 18.82
D) 21.65 and 28.35

Question

Quizplus · Accepted Answer

The values that have 25% of the observations below and above them are the first and third quartiles, respectively. In a normal distribution, these correspond to specific z-scores: approximately -0.675 for the first quartile and +0.675 for the third quartile. To find the actual values, use the formula: value = mean + (z-score * standard deviation). For the first quartile: 25 + (-0.675 * 5) = 21.625. For the third quartile: 25 + (0.675 * 5) = 28.375. These values are rounded to 21.65 and 28.35, respectively.

A Random Variable Is Normally Distributed with a Mean of 25