Questions: Provide an appropriate response. Use the Standard Normal Table to find the probability. 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 3,000. If a teacher is selected at random, find the probability that he or she makes more than 36,000. 0.1056 0.9082 0.4040 0.0912

Provide an appropriate response. Use the Standard Normal Table to find the probability.

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 3,000. If a teacher is selected at random, find the probability that he or she makes more than 36,000.
0.1056
0.9082
0.4040
0.0912

Transcript text: Provide an appropriate response. Use the Standard Normal Table to find the probability. 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. 0.1056 0.9082 0.4040 0.0912

Solution

Solution Steps

Step 1: Calculate the Cumulative Probability

To find the probability that a randomly selected teacher earns less than \$36,000, we compute the cumulative distribution function (CDF) at $ x = 36000 $. The result is:

\[ P(X \leq 36000) \approx 0.9088 \]

Step 2: Calculate the Probability of Earning More Than \$36,000

To find the probability that a teacher earns more than \$36,000, we use the complement of the cumulative probability:

\[ P(X > 36000) = 1 - P(X \leq 36000) \approx 1 - 0.9088 \approx 0.0912 \]