/*! 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. 23 23. ITBS scores The Normal distr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 23 (page 356)

23. ITBS scores The Normal distribution with mean 渭=6.8and standard deviation 蟽=1.6is a good description of the Iowa Test of Basic Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of a randomly chosen student Xfor short. Find P(X鈮�9)and interpret the result. Follow the four-step process.

Short Answer

Expert verified

The probability for P(X鈮�9)is 0.0838. There is 8.38%chances that student's score is 9or more.

Step by step solution

01

Given information

The Normal distribution with mean 渭=6.8and a standard deviation of 蟽=1.6.

02

Explanation

Let Xbe a random variable with a mean of 6.8and a standard deviation of 1.6and a normal distribution.

Thez-score is calculated by dividing the value reduced by the mean by the standard deviation:
z=x-渭蟽
Where, xindicates raw score, 渭indicates population mean, and蟽 indicates the population standard deviation.
P(X鈮�9)can be calculated as:

P(x鈮�9)=Px鈭�渭蟽鈮�9鈭�渭蟽=Pz鈮�9鈭�6.81.6=P(Z鈮�1.38)=0.0838

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

19. Housing in San Jose How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,
California:

Let X = the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student鈥檚 grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 10. Let G=the grade of a randomly chosen student in the class.

NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the median of G. Show your method.

(b) Find the IQR of G. Show your method.

(c) What shape would the probability distribution of Ghave? Justify your answer

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 T=X+Y.

Find and interpret 渭T.

Chess and reading (4.3) If the study found a statistically signi铿乧ant improvement in reading scores, could you conclude that playing chess causes an increase in reading skills? Justify your answer

18. Life insurance

(a) It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain \(1250in premiums. But if he were to die, you would lose almost \)100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.

(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the
investment. We can measure the great risk of insuring a single person鈥檚 life in Exercise 14by computing the standard deviation of the income Y that the insurer will receive. Find 蟽Y using the distribution and mean found in Exercise 14.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete 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.