Question

The scores on a psychology exam were normally distributed with a mean of 52 and a standard deviation of 6. About what percentage of scores were less than 40​?

Answer 1

Using the normal distribituion, it is found that 2.28% of of scores were less than 40.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.

• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are given by, respectively:

$\mu = 52, \sigma = 6$.

The proportion of scores that were less than 40​ is the p-value of Z when X = 40, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40 - 52}{6}$

$Z = -2$

$Z = -2$ has a p-value of 0.0228.

2.28% of of scores were less than 40.

More can be learned about the normal distribituion at https://brainly.com/question/24663213