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