Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 56 (page 430)

A uniform distribution has a minimum of six and a maximum of ten. A sample of 50is taken.

Find the 90th percentile for the sums.

Short Answer

Expert verified

The 90th percentile for the sum is410.4512.

Step by step solution

01

Given Information

Given a sample of 50 variables with uniform distribution U(6,10).

02

Calculation

If variable Zhas a uniform distribution on the interval [6,10], then the mean of Zis 8and the standard deviation is 1.1547.

Thus the allocation of the sums is:

N(50·8,50·1.1547)=N(400,8.165)

Finding the 90th percentile:

P(Σx<z)=0.9

PΣx-4008.165<z-4008.165=0.9

If variable Zhas a standard normal distribution, then

P(Z<1.28)=0.9

Thus,

z-4008.165=1.28

z-400=10.4512

z=410.4512.

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.

Start your free trial

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

An unknown distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let X=one object of interest.

What is P(Σx>9,000)?

Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18 to 24follow a normal distribution.
a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than120 .
b. If 40 women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120 .
c. If the sample were four women between the ages of 18to 24 and we did not know the original distribution, could the central limit theorem be used?

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

What is the distribution for the length of time one battery lasts?

According to Boeing data, the 757airliner carries 200passengers and has doors with a height of 72inches. Assume for a certain population of men we have a mean height of 69.0inches and a standard deviation of 2.8 inches.
a. What doorway height would allow 95%of men to enter the aircraft without bending?
b. Assume that half of the 200passengers are men. What mean doorway height satisfies the condition that there is a0.95probability that this height is greater than the mean height of 100men?

c. For engineers designing the 757 , which result is more relevant: the height from part a or part b? Why?

46. Draw the graph from Exercise 7.45
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.

Sign-up for free