Question

the scores on a test given to all juniors in a school district are normally distributed with a mean of 80 and a standard deviation of 8. Find the percent of juniors whose score is at least 80. The percent of juniors whose score is at or above the mean is_____% PLZ HELP!

Answer 1

The percent of juniors whose score is at or above the mean is 50%

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 80, \sigma = 8`

Find the percent of juniors whose score is at least 80.

This is 1 subtracted by the pvalue of Z when X = 80. So

`Z = (X - \mu)/(\sigma)`

`Z = (80 - 80)/(8)`

`Z = 0`

`Z = 0` has a pvalue of 0.5

1 - 0.5 = 0.5

So

The percent of juniors whose score is at or above the mean is 50%