Question

The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

Answer 1

Answer:

21.77% probability that a randomly selected teacher earns more than $525 a week

Step-by-step explanation:

Problems of normally distributed samples 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:

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

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:

$\mu = 490, \sigma = 45$

What is the probability that a randomly selected teacher earns more than $525 a week?

This is 1 subtracted by the pvalue of Z when X = 525. So

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

$Z = \frac{525 - 490}{45}$

$Z = 0.78$

$Z = 0.78$ has a pvalue of 0.7823

1 - 0.7823 = 0.2177

21.77% probability that a randomly selected teacher earns more than $525 a week