Question

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of​ $32,000 and a standard deviation of​ $3000. If a teacher is selected at​ random, find the probability that he or she makes more than​ $36,000.

Answer 1

Normal distribution table

Explanation:

We need to define all the variables that are presented to us in the problem, like this:

Data point in question = xi = 36000

The mean = μ = 32000

The standar variation = s = 3000

calculate the z-score for the left bound

x = 36000:

`z = (x_(i)-\mu)/((s)/(√(n)) )`

where μ = 32000, s = 3000, n = 1. (There is only one

teacher in the sample.)

z-score for 36000 is calculated thusly:

`z = (36000-32000)/(3000) =1.3333`

It is necessary to look in the normalized table for this value, and look in the area on the left that for 1.33 the result is 0.9082

So our probability is 0.9082 that he or she makes more than $36000