/*! 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. 5.8 A randomly chosen IQ聽test taker... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.8 (page 217)

A randomly chosen IQtest taker obtains a score that is approximately a normal random variable with mean 100and standard deviation 15. What is the probability that the score of such a person is

(a) more than 125;

(b) between 90and 110?

Short Answer

Expert verified

(a) Probability that the score of a person more than 125is 0.0478

(b) Probability that the score of a person between90and110is0.4972

Step by step solution

01

Step:1 Find the Probability that the score of a person more than 125 (part a)

Define Xas a random variable that represents a random person's IQ. We're told that data-custom-editor="chemistry" X~N100,152. That is, Y=X-10015has a conventional normal distribution with a cumulative distribution蠒.

P(X>125)=1-P(X鈮�125)=1-PX-10015鈮�125-10015

=1-桅53鈮�0.0478

02

Step:2 Find the Probability that the score of a person between 90 and 110 (part b)

P(X鈭�(90,110))=P(X鈮�110)-P(X鈮�90)

=PX-10015鈮�110-10015-PX-10015鈮�90-10015

=桅23-桅-23=2桅23-1=0.4972

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

Show that a plot of loglog(1-F(x))-1against logXwill be a straight line with slope 尾when F(-)is a Weibull distribution function. Show also that approximately 63.2percent of all observations from such a distribution will be less than 伪. Assume that v=0.

Let X be a continuous random variable having cumulative distribution function F. Define the random variable Y by Y = F(X). Show that Y is uniformly distributed over (0, 1).

A bus travels between the two cities A and B, which are 100miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a uniform distribution over (0,100). There is a bus service station in city A, in B, and in the center of the route between A and B. It is suggested that it would be more efficient to have the three stations located 25,50,and75miles, respectively, from A. Do you agree? Why?

Evidence concerning the guilt or innocence of a defendant in a criminal investigation can be summarized by the value of an exponential random variable X whose mean 渭 depends on whether the defendant is guilty. If innocent, 渭 = 1; if guilty, 渭 = 2. The deciding judge will rule the defendant guilty if X > c for some suitably chosen value of c.

(a) If the judge wants to be 95 percent certain that an innocent man will not be convicted, what should be the value of c?

(b) Using the value of c found in part (a), what is the probability that a guilty defendant will be convicted?

If Xis an exponential random variable with a parameter位=1, compute the probability density function of the random variable Ydefined by Y=logX
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.