Given a normally shaped distribution with a μ = 62 and a σ_M = 5, what is p(M 52)? A) .9772 B) .0228 C) .0047 D) .9953

Question

Given a normally shaped distribution with a μ = 62 and a σ_M = 5, what is p(M > 52)? A) .9772 B) .0228 C) .0047 D) .9953

Quizplus · Accepted Answer

To find $p(M > 52)$, we calculate the Z-score using the formula $Z = \frac{X - \mu}{\sigma}$, where $X = 52$, $\mu = 62$, and $\sigma = 5$. This gives us $Z = \frac{52 - 62}{5} = -2$. Looking up the Z-score of -2 in a standard normal distribution table or using a calculator, we find that the area to the left of Z = -2 is approximately .0228. Since we want $p(M > 52)$, we subtract this from 1 to get .9772, indicating that approximately 97.72% of the distribution is above 52.

Given a Normally Shaped Distribution with a μ = 62