Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

At the conclusion of training, all factory workers are timed as they complete a task. The completion times for the task are normally distributed.


Suppose a worker's completion time is 1.1 standard deviations above the mean. What is the worker's percentile score? Round your result to one decimal place.


The annual salaries for people in a particular profession are known to be normally distributed with a mean of $54,800 and a standard deviation of $2,600.

What percentage of people in this profession earn annual salaries between $54,000 and $57,000? Round your result to one decimal place.

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 hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.