Assume that the heights of women are normally distributed with a mean of 62.2 inches and a standard deviation of 2.3 inches. Find $\mathrm { Q } _ { 3 } ,$ the third quartile that separates the bottom 75% from the top 25%.
A)63.8
B)60.6
C)64.8
D)65.1

Question

Quizplus · Accepted Answer

The third quartile, $Q_3$, corresponds to the 75th percentile of a distribution. In a normal distribution, the 75th percentile can be found by using the Z-score table or formula for the standard normal distribution. The Z-score for the 75th percentile is approximately 0.674. Using the formula $X = \mu + Z\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $Z$ is the Z-score, we calculate $X = 62.2 + 0.674(2.3) = 62.2 + 1.6 = 63.8$.

Assume That the Heights of Women Are Normally Distributed with a Mean