Question

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. a. 0.4040 b. 0.1056 c. 0.0918 d. 0.9082

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 36000$, $\mu=32000$, and $\sigma = 3000$.
$z=\frac{36000 - 32000}{3000}=\frac{4000}{3000}\approx1.33$

Step2: Find the probability in the standard - normal table

The standard - normal table gives $P(Z\leq z)$. We want $P(Z > 1.33)$. Since the total area under the normal curve is 1, we use the property $P(Z>z)=1 - P(Z\leq z)$. Looking up $z = 1.33$ in the standard - normal table, $P(Z\leq1.33)=0.9082$. Then $P(Z > 1.33)=1 - 0.9082=0.0918$.

Answer:

C. 0.0918