Using the normal distribution, it is found that a production worker has to make $542.64 a week to be in the top 30% of wage earners.
<h3>Normal Probability Distribution</h3>In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of
.
- The standard deviation is of
.
- The lower bound of the top 30% is the 70th percentile, which is X when Z has a p-value of 0.7, so <u>X when Z = 0.84.</u>
A production worker has to make $542.64 a week to be in the top 30% of wage earners.
You can learn more about the normal distribution at brainly.com/question/24663213