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

Florida State University has 14statistics classes scheduled for its Summer 2013term. One class has space available for 30students, eight classes have space for 60students, one class has space for 70students, and four classes have space for 100students.

a. What is the average class size assuming each class is filled to capacity?

b. Space is available for 980students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable Xequal the size of the student’s class. Define the PDF for X.

c. Find the mean of X.

d. Find the standard deviation ofX.

Short Answer

Expert verified

a) The number of scholars are 70

b) The table containing variables Xand P(x)

c) The typical class size and also the mean is 70.

d) Variance is 20.702

Step by step solution

01

Given information (part a)

The number of classes which has a space for 30students=1

The number of classes which has a space for 60students=8

The number of classes which has a space for 70students=1

The number of classes which has a space for 100students=4

02

Explanation (part a)

The numberof scholars:

=30+8×60+70+4×10014=70

03

Given information (part b) 

The number of classes which has a space for 30students=1

The number of classes which has a space for 60students=8

The number of classes which has a space for 70students=1

The number of classes which has a space for 100students=4

04

Explanation (part b)

The category length is about by variable X. Tables containing variables and likelihood are offered as

X
P(X)
30
114
60
814
90
114
100
414
05

Given information (part c)

The number of classes which has a space for 30students=1

The number of classes which has a space for 60students=8

The number of classes which has a space for 70students=1

The number of classes which has a space for 100students=4

06

Explanation (part c)

Variable X has such a method value

μ=30114+60814+70114+100414=70

07

Given information (part d)

The number of classes which has a space for 30students=1

The number of classes which has a space for 60students=8

The number of classes which has a space for 70students=1

The number of classes which has a space for 100students=4

08

Explanation (part d)

Constant X's Variance was

σ=x(xμ)2P(x)=20.702

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

Use the following information to answer the next six exercises: On average, a clothing store gets 120customers per day.

What is the probability of getting 150customers in one day?

There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being \(1. The player places a bet on a number or object. The “house” rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)1 bet. If one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or her \(1 bet, plus \)1 profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her \(1 bet, plus \)2 profit. If all three dice show the number or object bet, the player gets back his or her \(1 bet, plus \)3 profit. Let X = number of matches and Y = profit per game.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. List the values that Y may take on. Then, construct one PDF table that includes both X and Y and their probabilities.

e. Calculate the average expected matches over the long run of playing this game for the player.

f. Calculate the average expected earnings over the long run of playing this game for the player

g. Determine who has the advantage, the player or the house.

Approximately 8%of students at a local high school participate in after-school sports all four years of high school. A group of 60seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of

high school.

a. In words, define the random variable X.

b. List the values that Xmay take on.

c. Give the distribution ofX.X~_____(_____,_____)

d. How many seniors are expected to have participated in after-school sports all four years of high school?

e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all

four years of high school.

f. Based on numerical values, is it more likely that four or that five of the seniors participated in after-school sports

all four years of high school? Justify your answer numerically.

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

a. What is the probability distribution for X?

b. Use your calculator to find the following probabilities:

i. the probability that 25 adults in the sample prefer saving over spending

ii. the probability that at most 20 adults prefer saving

iii. the probability that more than 30 adults prefer saving

c. Using the formulas, calculate the

(i) mean and

(ii) standard deviation of X.

Jeremiah has basketball practice two days a week. Ninety percent of the time, he attends both practices. Eight percent of the time, he attends one practice. Two percent of the time, he does not attend either practice. What is X and what values does it take on?

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