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?
A)0.2177
B)0.1003
C)0.2823
D)0.7823

Question

Quizplus · Accepted Answer

The probability that a randomly selected teacher earns more than $525 a week is the area under the normal distribution curve to the right of $525. This area is equal to 1 - P(X < 525), where X is the random variable representing the weekly salary of a teacher. Using the standard normal distribution (z-distribution), we have:z = (525 - 490) / 45 = 0.78P(X < 525) = P(Z < 0.78) = 0.7823Therefore, the probability that a randomly selected teacher earns more than $525 a week is 1 - 0.7823 = 0.2177.

The Weekly Salaries of Teachers in One State Are Normally