A normal population has a mean $\mu = 40$ and standard deviation $\sigma = 11$. What proportion of the population is between 24 and $32 ?$
A) 0.8408
B) 0.0735
C) 0.1592
D) 0.2327

Question

Quizplus · Accepted Answer

To find the proportion of the population between 24 and 32, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$. For X = 24, $Z = \frac{24 - 40}{11} = -1.45$. For X = 32, $Z = \frac{32 - 40}{11} = -0.73$. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the area (proportion of the population) between these Z-scores is approximately 0.1592.

A Normal Population Has a Mean μ=40\mu = 40μ=40 And Standard Deviation

A Normal Population Has a Mean $\mu = 40$ And Standard Deviation