Question

Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard deviation of $4000. Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that randomly chosen salary exceeds $40,000

Answer 1

0.62% probability that randomly chosen salary exceeds $40,000

Explanation:

Problems of normally distributed distributions are 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 question:

`\mu = 30000, \sigma = 4000`

What is the probability that randomly chosen salary exceeds $40,000

This is 1 subtracted by the pvalue of Z when X = 40000. So

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

`Z = (40000 - 30000)/(4000)`

`Z = 2.5`

`Z = 2.5` has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that randomly chosen salary exceeds $40,000