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 first quartile of height in this Distribution? Round your answer to two decimal places.
A) 25 inches
B) 66.31 inches
C) 67.25 inches
D) 69.34 inches
E) None of the above.

Question

Quizplus · Accepted Answer

The first quartile (Q1) in a normal distribution can be found using the Z-score table. The first quartile corresponds to the 25th percentile, which has a Z-score of approximately -0.675. Using the formula: X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score, we calculate the first quartile as follows: X = 68 + (-0.675)(2.5) = 66.31 inches.

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