Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are at least $74,000?

84.13% of of salaries that are at least $74,000

Step-by-step explanation:

Problems of normally distributed(bell-shaped) samples can be 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 problem, we have that:

What can be said about the percentage of salaries that are at least $74,000?

has a pvalue of 0.1587.

1 - 0.1587 = 0.8413

84.13% of of salaries that are at least $74,000