A normal population has a mean $\mu = 14$ and standard deviation $\sigma = 2$ . What is the 43rd percentile of the population?
A) 15.00
B) 12.28
C) 16.37
D) 13.64

Question

Quizplus · Accepted Answer

To find the 43rd percentile of a normal distribution, we use the Z-score formula and look up the corresponding Z-score for the 43rd percentile in a standard normal distribution table. The 43rd percentile corresponds to a Z-score of approximately -0.176. Using the formula $X = \mu + Z\sigma$, where $X$ is the value at the 43rd percentile, $\mu = 14$, $\sigma = 2$, and $Z = -0.176$, we calculate $X = 14 + (-0.176)(2) = 14 - 0.352 = 13.648$. Rounding to two decimal places, the closest answer is 13.64.

A Normal Population Has a Mean μ=14\mu = 14μ=14 And Standard Deviation

A Normal Population Has a Mean $\mu = 14$ And Standard Deviation