Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.
-The monthly incomes of trainees at a local mill are normally distributed, with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $875 a month?

Question

Quizplus · Accepted Answer

To find the percentage of trainees earning less than $875, we calculate the z-score using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the value in question ($875), $\mu$ is the mean ($1,100), and $\sigma$ is the standard deviation ($150). Plugging in the values, we get $z = \frac{875 - 1100}{150} = -1.5$. Looking up a z-score of -1.5 in a standard normal distribution table or using a calculator, we find that approximately 6.68% of the distribution falls below this z-score. This means about 6.68% of trainees earn less than $875 a month.

Find the Indicated Percentage for the Normally Distributed Variable