Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Yoonie is a personnel manager in a large corporation. Each month she must review 16of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let x-be the random variable representing the meantime to complete the 16reviews. Assume that the 16reviews represent a random set of reviews.

Find the probability that one review will take Yoonie from 3.5to 4.25hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability

b. P(________ <x< ________) = _______

Short Answer

Expert verified

From the information above

a) The probability that one review will take Yoonie from 3.5to 4.25hours is 0.2459. and the shaded region corresponding to the probability is:

b)p(3.5<x<4.25)=0.2459

Step by step solution

01

Given Information (part a)

It is provided that Yoonie reviews 16of the employees with an average time of 4hours and a standard deviation of 1.2hours. We have to find the probability that Yoonie will take 3.5to 4.25hours for one review and graph it.

02

Step 2: Explanation(part a)

According to the information, we have to find the probability that one review will take Yoonie from 3.5 to 4. 25

The Computation of the probability is given as below:

p(3.5<x<4.25)=p(Z<4.5μσ)p(Z<3.5μσ)

=p(Z<4.2541.2)p(Z<3.541.2)

=p(Z<0.21)p(Z<0.42)

Therefore,

localid="1648621489396" p(z<0.21)and

p(Z<0.42)in Excel is:

03

Step 3: Shaded region representation (part a)

Therefore,

p(3.5<x<4.25)=p(Z<0.21)p(Z<1.42)

=0.58320.3372

=0.2459

The shaded region corresponding to the probability is as shown below:

04

Given Information (part b)

It is provided that Yoonie reviews 16of the employees with an average time of 4hours and a standard deviation of1.2 hours

05

Explanation (part b)

The probability is

p(3.5<x<4.25)=p(Z<0.21)p(Z<1.42)

=0.58320.3372

Simplify,

localid="1648621737422" =0.2459

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A typical adult has an average IQ score of 105with a standard deviation of 20. If 20randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between 85 and 125 points?

Suppose that it is past noon on a delivery day, The probability that a person must wait at least one and half more hours is;

a.14

b. 12

c. 34

d.38

Yoonie is a personnel manager in a large corporation. Each month she must review 16of the employees. From past experience, she has found that the reviews take her approximately four-hour search to do with a population standard deviation of 1.2hours . Let Χ be the random variable representing the time it takes her to complete one review.Assume Χ is normally distributed. Let x-be the random variable representing the meantime to complete the 16reviews. Assume that the 16reviews represent a random set of reviews

Complete the distributions.

a. X~ _____(_____,_____)

b. x-~ _____(_____,_____)

According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040is 10.53hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36taxpayers.

a. In words, Χ=_____________

b. In words,X=_____________

c. X¯~_____(_____,_____)

d. Would you be surprised if the 36taxpayers finished their Form 1040s in an average of more than 12hours? Explain why or why not in complete sentences.

e. Would you be surprised if one taxpayer finished his or her Form 1040in more than 12hours? In a complete sentence, explain why.

Your company has a contract to perform preventive maintenance on thousands of air-conditioners in a large city. Based on service records from previous years, the time that a technician spends servicing a unit averages one hour with a standard deviation of one hour. In the coming week, your company will serve a simple random sample of 70 units in the city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free