A variable is normally distributed with a hypothesized population mean of 30 and a standard deviation of 4. What percentage of scores are greater than 37?
A) 1.75%
B) 4.01%
C) 45.99%
D) 51.75%

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the standard normal distribution formula:

z = (x - μ) / σ

where: 
z = the z-score 
x = the score we are interested in (which is 37) 
μ = the hypothesized population mean (which is 30) 
σ = the standard deviation (which is 4)

Plugging in these values, we get:

z = (37 - 30) / 4 
z = 1.75

Now we need to find the percentage of scores greater than 37. We can use a standard normal distribution table or calculator to look up the area to the right of z = 1.75. This area represents the percentage of scores greater than 37.

Using the table (or a calculator), we find that the area to the right of z = 1.75 is 0.0401.

Therefore, the answer is: 
Answer: B

A Variable Is Normally Distributed with a Hypothesized Population Mean