The height of an 18-year old student at your university has an approximate normal distribution with a mean of 68 inches and a standard deviation of 2.5 inches. What is the third quartile of height in this Distribution? Round your answer to two decimal places.
A) 63 inches
B) 65.5 inches
C) 69.69 inches
D) 72.42 inches
E) None of the above.

Question

Quizplus · Accepted Answer

The third quartile (Q3) in a normal distribution can be found using the Z-score table. The third quartile corresponds to the 75th percentile, which has a Z-score of approximately 0.674. Using the formula for converting Z-scores to raw scores, $X = \mu + Z\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $Z$ is the Z-score, we get $X = 68 + 0.674(2.5) = 68 + 1.685 = 69.69$ inches.

The Height of an 18-Year Old Student at Your University