/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 6.12 Using the information from Examp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 6.12 (page 378)

Using the information from Example 6.12, answer the following:

  1. The middle 40%of mandarin oranges from this farm is between __ and __.
  2. Find the 16thpercentile and interpret it in a complete sentence

Short Answer

Expert verified
  1. The middle 40%of mandarin oranges from this farm are between 5.72424and5.97576in diameter.
  2. The table value of the 16th percentile islocalid="1649343002299" 5.61

Step by step solution

01

Given Information (Part-a)

Given in the question that, X follows Normal distribution with,

渭=5.85

蟽=0.24

02

Solution of the Problem (Part-a)

For the middle40%data,

Let a and b be the limits

P[a<X<b]=0.40

1鈭�P[a<X<b]=1鈭�0.40=0.60

Due to symmetry,

P[X<a]=0.30andP[X>b]=0.30

For standard normal variable z, using z table we can say that.,

P[Z<鈭�0.524]=0.30and P[Z>0.524]=0.30

Using zthe score formula,

localid="1648298928299" a=渭+(z蟽)=5.85+(鈭�0.524脳0.24)=5.72424

localid="1648298940022" b=渭+(z蟽)=5.85+(0.524脳0.24)=5.97576

03

Given Information (Part-b)

Given in the question that,Xfollows Normal distribution with,

渭=5.85

蟽=0.24

04

Solution of the Problem (Part-b)

Compute the 16thpercentile as follow:

P(x<k)=0.16

Px鈭�渭蟽<k鈭�渭蟽=0.16

PZ<k鈭�5.850.24=0.16

k鈭�5.850.24=鈭�0.9945From standardnormal table

k鈭�5.85=鈭�0.9945脳0.24

k=鈭�0.23868+5.85

k鈮�5.61

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 91影视!

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

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean 碌=125and standard deviation 蟽=14. Systolic blood pressure for males follows a normal distribution.

a. Calculate the z-scores for the male systolic blood pressures 100and 150millimeters.

b. If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 150 millimeters, what would you say to him?

About what percent ofx values lie between the mean and one standard deviation?

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space?

a. Yes

b. No

c. Unable to determine

The heights of the 430National Basketball Association players were listed on team rosters at the start of the 2005鈥�2006season. The heights of basketball players have an approximately normal distribution with mean, 碌=79inches and a standard deviation, 蟽=3.89inches. For each of the following heights, calculate the z-score and interpret it using complete sentences

a. 77inches

b. 85inches

c. If an NBA player reported his height had a z-score of 3.5, would you believe him? Explain your answer

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
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.