/*! 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. 44 Researchers carried out a survey... [FREE SOLUTION] | 91影视

91影视

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Suppose we select one of these students at random. What鈥檚 the probability of each of the following?

a. The student is a sixth-grader or rated good grades as important.

b. The student is not a sixth-grader and did not rate good grades as important.

Short Answer

Expert verified

Part a. Probability,

P(6thgradeorGrades)0.6985

Part b. Probability,

P(Not6thgraderandnoGrades)0.3015

Step by step solution

01

Part a. Step 1. Given information

Survey data:

02

Part a. Step 2. Explanation

Look at the bottom right corner of the table,

There are 335students in total.

Thus,

The number of possible outcomes is 335.

Also,

For the student who are rated good grades or 6th grader,

Add up all the values in column 鈥淕rades鈥 and row 鈥6th grade鈥, we will get 234in total.

Thus,

The number of favorable outcomes is 234.

Now,

The number of favorable outcomes divided by the number of possible outcomes gives the probability.

P(6thgradeorgrades)=NumberoffavorableoutcomesNumberofpossibleoutcomes=234335=0.6985

03

Part b. Step 1. Explanation

Look at the bottom right corner of the table,

There are 335students in total.

Thus,

The number of possible outcomes is 335.

Also,

For the student who did not rate good grades and not a 6th grader as well,

Add up all the values of 4th and 5th grades in the columns 鈥淎thletic鈥 and 鈥淧opular鈥, we will get 101in total.

Thus,

The number of favorable outcomes is 101.

Now,

The number of favorable outcomes divided by the number of possible outcomes gives the probability.

P(Not6thgraderandnogrades)=NumberoffavorableoutcomesNumberofpossibleoutcomes=1013350.3015

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

Suppose a loaded die has the following probability model:

If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1?

a. 0.10

b. 0.17

c. 0.30

d. 0.50

e. 0.60

BMI (2.2, 5.2, 5.3) Your body mass index (BMI) is your weight in kilograms divided by

the square of your height in meters. Online BMI calculators allow you to enter weight in

pounds and height in inches. High BMI is a common but controversial indicator of being

overweight or obese. A study by the National Center for Health Statistics found that the

BMI of American young women (ages 20 to 29) is approximately Normally distributed

with mean 26.8 and standard deviation 7.4.

27

a. People with BMI less than 18.5 are often classed as 鈥渦nderweight.鈥 What percent of

young women are underweight by this criterion?

b. Suppose we select two American young women in this age group at random. Find the

probability that at least one of them is classified as underweight.

Double fault!A professional tennis player claims to get 90%of her second serves in. In a recent match, the player missed 5of her first 20second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a 0.10probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss 5or more of her first 20second serves.

a. Describe how to use a random number generator to perform one trial of the simulation. The dot plot displays the number of second serves missed by the player out of the first 20second serves in simulated matches.

b. Explain what the dot at 6represents.

c. Use the results of the simulation to estimate the probability that the player would miss 5or more of her first 20second serves in a match.

d. Is there convincing evidence that the player misses more than 10%of her second serves? Explain your answer.

Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits鈥攃lubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as 鈥渇ace cards.鈥 Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

Type of card

Face cardNon-Face cardTotal
Heart3
10
13
Non-Heart9
30
39
Total12
40
52

Are the events 鈥渉eart鈥 and 鈥渇ace card鈥 independent? Justify your answer.

Butter side down Refer to the preceding exercise. Maria decides to test this

probability and drops 10 pieces of toast from a 2.5-foot table. Only 4of them land butter

side down. Maria wants to perform a simulation to estimate the probability that 4or

fewer pieces of toast out of 10would land butter side down if the researchers鈥 0.81

probability value is correct.

a. Describe how you would use a table of random digits to perform the simulation.

b. Perform 3trials of the simulation using the random digits given. Copy the digits onto

your paper and mark directly on or above them so that someone can follow what you

did.

29077
14863
61683
47052
62224
51025
95052
90908
73592
75186
87136
95761
27102
56027
55892
33063
41842
81868

c. The dotplot displays the results of 50 simulated trials of dropping 10pieces of toast.

Is there convincing evidence that the researchers鈥 0.81probability value is incorrect?

Explain 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.