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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

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.

Income tax returns Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a recent year:

a. What is the probability that a randomly chosen return shows an adjusted gross income of \(50,000 or more?

b. Given that a return shows an income of at least \)50,000, what is the conditional

probability that the income is at least $100,000?

Treating low bone density Fractures of the spine are common and serious

among women with advanced osteoporosis (low mineral density in the bones). Can taking

strontium ranelate help? A large medical trial was conducted to investigate this question.

Researchers recruited 1649women with osteoporosis who had previously had at least one

fracture for an experiment. The women were assigned to take either strontium ranelate or a

placebo each day. All the women were taking calcium supplements and receiving standard

medical care. One response variable was the number of new fractures over 3years.

a. Describe a completely randomized design for this experiment.

b. Explain why it is important to keep the calcium supplements and medical care the same

for all the women in the experiment.

c. The women who took strontium ranelate had statistically significantly fewer new

fractures, on average, than the women who took a placebo over a 3鈥year period. Explain

what this means to someone who knows little statistics.

Who eats breakfast?Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, 鈥淒o you eat breakfast on a regular basis?鈥 All 595students in the school responded to the survey. The resulting data are shown in the two-way table.

Suppose we select a student from the school at random. Define event Fas getting a female student and event Bas getting a student who eats breakfast regularly.

a. Find P(BC)

b. Find P(FandBC). Interpret this value in context.

c. Find P(ForBC).

Dogs and cats In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household.

a. Make a Venn diagram to display the outcomes of this chance process using events D: owns a dog, and C: owns a cat.

b. Find P(D鈭CC).
See all solutions

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