A normal population has a mean $\mu = 30$ and standard deviation $\sigma = 9$ . What proportion of the population is between 23 and 32?
A) 0.6306
B) 0.2177
C) 0.3694
D) 0.5871

Question

Quizplus · Accepted Answer

We need to find the proportion of the population that falls within the range of 23 to 32. First, we need to standardize the range using the formula:

z = (x - mu) / sigma

Plugging in the values, we get:

z1 = (23 - 30) / 9 = -0.7778
z2 = (32 - 30) / 9 = 0.2222

Next, we need to find the area under the standard normal curve between these two z-scores. Using a standard normal table or a calculator, we can find:

Area between -0.7778 and 0.2222 = 0.3694

Therefore, the proportion of the population between 23 and 32 is 0.3694 or approximately 0.37. The closest answer choice is C.

A Normal Population Has a Mean μ=30\mu = 30μ=30 And Standard Deviation

A Normal Population Has a Mean $\mu = 30$ And Standard Deviation