Solve the problem.
-Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. What percentage of people in that profession earn less than $48,000?
A) $1.50 \%$
B) $6.68 \%$
C) $55.96 \%$
D) $93.32 \%$

Question

Solve the problem.
-Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. What percentage of people in that profession earn less than $48,000? 
A) $1.50 \%$
B) $6.68 \%$
C) $55.96 \%$
D) $93.32 \%$

Quizplus · Accepted Answer

To find the percentage of people earning less than $48,000, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value in question ($48,000), $\mu$ is the mean ($45,000), and $\sigma$ is the standard deviation ($2,000). Plugging in the values, we get $Z = \frac{48,000 - 45,000}{2,000} = 1.5$. Looking up 1.5 in a standard normal distribution table or using a calculator, we find that approximately 93.32% of the distribution falls below a Z-score of 1.5. This means that about 93.32% of people in that profession earn less than $48,000.

Solve the Problem 1.50%1.50 \%1.50% B) 6.68%6.68 \%6.68% C) 55.96%55.96 \%55.96% D) 93.32%93.32 \%93.32%

Solve the Problem $1.50 \%$ B) $6.68 \%$ C) $55.96 \%$ D) $93.32 \%$