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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- 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>
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.84 = \frac{X - 441.84}{120}](https://tex.z-dn.net/?f=0.84%20%3D%20%5Cfrac%7BX%20-%20441.84%7D%7B120%7D)
![X - 441.84 = 0.84(120)](https://tex.z-dn.net/?f=X%20-%20441.84%20%3D%200.84%28120%29)
![X = 542.64](https://tex.z-dn.net/?f=X%20%3D%20542.64)
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
Answer:
earth venus mars mercury
Step-by-step explanation:
2x - 4y = 10
7x - 9y = 12
_________
9x - 5y = 2
Answer: 5/24
Step-by-step explanation:
First:
Reduce fractions where possible.
Then your initial equation becomes:
5/16 * 2/3
Second:
Applying the fractions formula for multiplication,
5*2 and 16*3 = 10/48
Simplifying 10/48, the answer is
5/24