Question

Find the indicated probability. 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?

1) 0.7823
2) 0.2823
3) 0.1003
4) 0.2177

Answer 1

To find the probability of a teacher earning more than $525, we calculate the z-score and use the standard normal distribution table. The correct probability is 0.2177, indicating that option 4) is the correct answer.

Step-by-step explanation:

The question is about finding the probability that a teacher earns more than a certain amount, given that salaries are normally distributed. To solve this, we calculate the z-score that corresponds to a salary of $525, given a mean salary of $490 and a standard deviation of $45. The z-score is computed as follows:

Z = (X - μ) / σ

Where X is the salary we're interested in, μ is the mean salary, and σ is the standard deviation. Plugging the values into the formula:

Z = ($525 - $490) / $45 ≈ 0.78

Next, we use the standard normal distribution table to find the probability that Z is greater than 0.78. This probability corresponds to the area under the curve to the right of Z = 0.78. The area to the left of Z = 0.78 is 0.7823. Therefore, the area to the right, which is our desired probability, is 1 - 0.7823 = 0.2177. Thus, option 4) is the correct answer.