Find the specified percentile, quartile, or decile.
-Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of the third quartile.
A)64.3 inches
B)66.1 inches
C)67.8 inches
D)65.3 inches

Question

Find the specified percentile, quartile, or decile.
-Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of the third quartile. 
A)64.3 inches
B)66.1 inches
C)67.8 inches
D)65.3 inches

Quizplus · Accepted Answer

The third quartile (Q3) corresponds to the 75th percentile in a distribution. In a normal distribution, the 75th percentile can be found using the Z-score table or a calculator with the mean and standard deviation. The Z-score for the 75th percentile is approximately 0.674. Using the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score, we calculate X = 63.6 + (0.674)(2.5) = 63.6 + 1.685 = 65.285 inches, which rounds to 65.3 inches, making option D correct.

Find the Specified Percentile, Quartile, or Decile