Test scores are normally distributed with a mean of 500. Convert the given score to a z-score, using the given standard deviation. Then find the percentage of students
who score below 620, if the standard deviation is 80.

The percentage of students who scored below 620 is 93.32%.

Step-by-step explanation:

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

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

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 question, we have that:

Percentage of students who scored below 620:

This is the pvalue of Z when X = 620. So

has a pvalue of 0.9332

The percentage of students who scored below 620 is 93.32%.

a is the correct