If the mean salary of high school teachers In the United States is $42,335 and the standard deviation is 2,000 the probability that a randomly selected teacher will make more than $40,542 per year

The probability that a randomly selected teacher will make more than $40,542 per year is 0.82

Step-by-step explanation:

Looking at the information given, the population mean and population standard deviation are known. We would apply the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = $42335

σ = 2000

x = $40542

The probability that a randomly selected teacher will make more than $40,542 per year is expressed as

P(x > 40542) = 1 - P(x ≤ 40542)

For P(x ≤ 40542),

z = (40542 - 42335)/2000 = - 0.9

Looking at the normal distribution table, the probability corresponding to the z score is 0.18

P(x > 40542) = 1 - 0.18 = 0.82