Question

The scores on a standardized exam are normally distributed with a mean of 400 and a standard deviation of 50.

Answer 1

Using the normal distribution, it is found that approximately 40% of the scores are greater than 413.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, we have that the mean and the standard deviation of the scores are given by:

$\mu = 400, \sigma = 50$

Approximately 40% of the scores are greater than the 60th percentile, which is X when Z = 0.253.

Then:

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

$0.253 = \frac{X - 400}{50}$

X - 400 = 50(0.253)

X = 412.65.

Rounding up, approximately 40% of the scores are greater than 413.

More can be learned about the normal distribution at brainly.com/question/24663213

#SPJ1