Question

The graph shows a nonstandard normal distribution curve with

Answer 1

Using the normal distribution, it is found that the area of the shaded region is of 0.7823.

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 is of 59, hence $\mu = 59$.

• The standard deviation is of 7, hence $\sigma = 7$.

The shaded region is the region to the left of 64.2, hence it's area is the p-value of Z when X = 64.2.

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

$Z = \frac{64.2 - 59}{6.7}$

$Z = 0.7761$

$Z = 0.7761$ has a p-value of 0.7823.

The area of the shaded region is of 0.7823.

To learn more about the normal distribution, you can take a look at brainly.com/question/24663213