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Chapter 5: Q. 44 (page 327)

Middle school values 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

a. The probability that the student is a sixth 鈭 grader or rated good grades as important is0.6985

b. The probability that the student is not a sixth 鈭 grader and did no rate good grades as important is 0.3015

Step by step solution

01

Part (a) Step 1 : Given Information

We have to determine the probability that the student is a sixth 鈭 grader or rated good grades as important.

02

Part (a) Step 2 : Simplification

Take a look at the table's bottom right corner.
In total, 335students are enrolled.
Thus,
There are 335different outcomes to choose from.
Also,
For students who have received good grades or are in the sixth grade,
We'll obtain 234total if we add all the values in column "Grades" and row "6thgrade."
Thus,
There are a total of 234positive outcomes.
Now,
The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

P(6th鈥grade鈥or鈥Grades)=Number鈥of鈥favourable鈥outcomesNumber鈥of鈥possible鈥outcomes鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥=234335鈥鈥鈮0.6985

03

Part (b) Step 1 : Given Information

We have to determine the probability that the student is not a sixth 鈭 grader and did no rate good grades as important.

04

Part (b) Step 2 : Simplification

Take a look at the table's bottom right corner.
In total, 335students are enrolled.
Thus,
There are 335different outcomes to choose from.
Also,
For the pupil who did not have good grades and was not in sixth grade,
We'll get 101if we add all the values from the 4thand 5thgrades in the columns "Athletic" and "Popular."
Thus,
The total number of positive outcomes is 101.
Now,
The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

P(Not鈥6th鈥grader鈥and鈥no鈥Grades)=Number鈥of鈥favourable鈥outcomesNumber鈥of鈥possible鈥outcomes鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥鈥=101335鈥鈥鈥鈥鈮0.3015

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Most popular questions from this chapter

The most common bet in craps is the 鈥減ass line.鈥 A pass line bettor wins immediately if either a 7or an11comes up on the first roll. This is called a natural. What is the probability that a natural does not occur?

a. 2/36

b.6/36

c.8/36

d. 16/36

e. 28/36

You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is approximately 0.11. This means that

a. in every 100bridge deals, each player has 1ace exactly 11times.

b. in 1million bridge deals, the number of deals on which each player has 1ace will be exactly 110,000.

c. in a very large number of bridge deals, the percent of deals on which each player has 1ace will be very close to 11%.

d. in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11.

e. If each player gets an ace in only 2of the first 50deals, then each player should get an ace in more than 11%of the next 50deals.

Suppose that a student is randomly selected from a large high school. The probability

that the student is a senior is 0.22. The probability that the student has a driver鈥檚 license

is 0.30. If the probability that the student is a senior or has a driver鈥檚 license is 0.36,

what is the probability that the student is a senior and has a driver鈥檚 license?

a.0.060b.0.066c.0.080d.0.140e.0.160

Taking the train According to New Jersey Transit, the 8:00A.M.weekday train from Princeton to New York City has a 90%chance of arriving on time. To test this claim, an auditor chooses 6weekdays at random during a month to ride this train. The train arrives late on 2of those days. Does the auditor have convincing evidence that the company's claim is false? Describe how you would carry out a simulation to estimate the probability that a train with a 90%chance of arriving on time each day would be late on 2or more of 6days. Do not perform the simulation.

Lefties A website claims that 10%of U.S. adults are left-handed. A researcher believes that this figure is too low. She decides to test this claim by taking a random sample of 20U.S. adults and recording how many are left-handed. Four of the adults in the sample are left-handed. Does this result give convincing evidence that the website鈥檚 10%claim is too low? To find out, we want to perform a simulation to estimate the probability of getting 4or more left-handed people in a random sample of size 20from a very large population in which 10%of the people are left-handed.

Let 00to 09indicate left-handed and 10to 99 represent right-handed. Move left to Page Number: 311right across a row in Table D. Each pair of digits represents one person. Keep going until you get20 different pairs of digits. Record how many people in the simulated sample are left-handed. Repeat this process many, many times. Find the proportion of trials in which4 or more people in the simulated sample were left-handed.
See all solutions

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