Use technology to solve the following problem: A normal population has a mean $\mu = 28$ and standard deviation $\sigma = 8$ What is the 58th percentile of the population?
A) 29.60
B) 26.64
C) 32.56
D) 35.52

Question

Quizplus · Accepted Answer

To find the 58th percentile of a normal distribution with a mean ($\mu$) of 28 and a standard deviation ($\sigma$) of 8, you can use a Z-table or a statistical calculator. The 58th percentile corresponds to a Z-score that can be found by looking up the percentile in a Z-table or using an inverse normal function in a calculator. Using the formula for converting Z-scores to raw scores, $X = \mu + Z\sigma$, where $X$ is the raw score, $\mu$ is the mean, $Z$ is the Z-score, and $\sigma$ is the standard deviation. For the 58th percentile, the Z-score is approximately 0.20 (since 0.58 corresponds to a Z-score of about 0.20 in the standard normal distribution). Plugging in the values: $X = 28 + 0.20(8) = 29.6$.

Use Technology to Solve the Following Problem: a Normal Population μ=28\mu = 28μ=28

Use Technology to Solve the Following Problem: a Normal Population $\mu = 28$