/*! 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.8 聽Days聽01234567聽Probability聽0... [FREE SOLUTION] | 91影视

91影视

Days01234567Probability0.680.050.070.080.050.040.010.02

Working out Refer to Exercise 6. Consider the events A = works out at least once and B = works out less than 5 times per week.

(a) What outcomes makeup event A? What is P(A)?

(b) What outcomes make up event B? What is P(B)?

(c) What outcomes make up the event 鈥淎 and B鈥? What is P(A and B)? Why is this probability not equal to P(A) 路 P(B)?

Short Answer

Expert verified

a)The probability of P(A)isrole="math" localid="1649478583105" 0.32

b)the probability of P(B)is0.93

c)P(AandB)P(A)P(B)because the events are not independent.

Step by step solution

01

Part (a) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

02

Part (a) Step 2: Calculation 

Consider Aas the event that depicts the workout at least once.

The outcomes for the event Acan be written as:

Outcomes={1,2,3,4,5,6,7}

P(A)can be calculated as:

localid="1649992396909" P(A)=P(X=1)+P(X=2)+..+P(X=7)=0.05+0.08+..+0.02=0.32

03

Part (b) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

04

Part (b) Step 2: Calculation 

Consider Aas the event that depicts the workout less than 5times in a week.

The outcomes for the event localid="1649992417188" Bcan be written as:

Outcomes={0,1,2,3,4}

P(B)can be calculated as:

localid="1649992420222" P(B)=P(X=0)+P(X=1)+..+P(X=4)=0.68+0.05++0.05=0.93

05

Part (c) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

06

Part (c) Step 2: Calculation 

Using the data of the above parts, the outcomes for the event Aand Bcan be written as:

Outcomes={1,2,3,4}

P(Aand B)can be calculated as:

localid="1649992432843" P(AandB)=P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.05+0.07+0.08+0.05=0.25

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 length in inches of a cricket chosen at random from a field is a random variable Xwith mean 1.2inches and standard deviation of 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 centimeters in an inch.

Benford鈥檚 law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.

(b) The first digits of randomly selected expense amounts actually follow Benford鈥檚 law (Exercise 5). What鈥檚 the expected value of the first digit? Explain how this information could be used to detect a fake expense report.

(c) What鈥檚 P(Y>6)? According to Benford鈥檚 law, what proportion of first digits in the employee鈥檚 expense amounts should be greater than 6? How could this information be used to detect a fake expense report?

Refer to the previous Check Your Understanding (page 390) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

3. What's the probability that the number of Patti's correct guesses is more than 2standard deviations above the mean? Show your method.

A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold? (a) 13%

(b) 20%

(c) 45%

(d) 55%

(e) 80%

86.1in 6wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, 鈥淧lease try again,鈥 while others said, 鈥淵ou鈥檙e a winner!鈥 The company advertised the promotion with the slogan 鈥1in6wins a prize.鈥 Suppose the company is telling the truth and that every 20-ounce
bottle of soda it fills has a1-in-6chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X= the number who win a prize.
(a) Explain why X is a binomial random variable.
(b) Find the mean and standard deviation of X. Interpret each value in context.

(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company鈥檚 1-in-6 claim inaccurate? Compute P(X3) and use the result to justify your answer.

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.