Explore a wide range of topics and get answers from experts on IDNLearn.com. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
Using the normal distribution, it is found that:
- The worker's score is at the 86.4th percentile.
- 42.2% of people in this profession earn annual salaries between $54,000 and $57,000.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- 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.
Question 1:
1.1 standard deviations above the mean, hence, a z-score of Z = 1.1.
- Looking at the z-table, z = 1.1 has a p-value of 0.864, hence, the worker's score is at the 86.4th percentile.
Question 2:
- Mean of 54800, hence [tex]\mu = 54800[/tex]
- Standard deviation of 2600, hence [tex]\sigma = 2600[/tex].
The proportion is the p-value of Z when X = 57000 subtracted by the p-value of Z when X = 54000, then:
X = 57000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57000 - 54800}{2600}[/tex]
[tex]Z = 0.846[/tex]
[tex]Z = 0.846[/tex] has a p-value of 0.801.
X = 54000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{54000 - 54800}{2600}[/tex]
[tex]Z = -0.307[/tex]
[tex]Z = -0.307[/tex] has a p-value of 0.379.
0.801 - 0.379 = 0.422
0.422 x 100% = 42.2%
42.2% of people in this profession earn annual salaries between $54,000 and $57,000.
A similar problem is given at https://brainly.com/question/24663213
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.
