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Chapter 5: Q. T5.7 (page 357)

The partially complete table that follows shows the distribution of scores on the AP庐

Statistics exam for a class of students.

Select a student from this class at random. If the student earned a score of 3 or higher

on the AP庐 Statistics exam, what is the probability that the student scored a 5?

a.0.150b.0.214c.0.300d.0.428e.0.700

Short Answer

Expert verified

The correct option is:

b.0.214is the probability that the student scored a5

Step by step solution

01

Given information

We have to find the is the probability that the student scored a5.

02

Explanation

Assuming that a single person cannot have more than one score, we may use the addition rule to solve for mutually exclusive events:

P(Score is at least3)=P(Score is3)+P(Score is4)+P(Score is5)

=0.70

P(Score is5鈭�Score is at least3)=P(Score is5and Score is at least3)P(Score is at least3)

=1570

鈮�0.214

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Most popular questions from this chapter

Recycling Do most teens recycle? To find out, an AP庐 Statistics class asked an SRS of 100students at their school whether they regularly recycle. In the sample, 55students said that they recycle. Is this convincing evidence that more than half of the students at the school would say they regularly recycle? The dotplot shows the results of taking 200SRSS of 100students from a population in which the true proportion who recycle is 0.50.

a. Explain why the sample result (55out of 100said "Yes") does not give convincing evidence that more than half of the school's students recycle.

b. Suppose instead that 63students in the class's sample had said "Yes." Explain why this result would give convincing evidence that a majority of the school's students recycle.

Notebook check Every 9weeks, Mr. Millar collects students' notebooks and checks their homework. He randomly selects 4different assignments to inspect for all of the students. Marino is one of the students in Mr. Millar's class. Marino completed 20homework assignments and did not complete 10assignments. He is surprised when Mr. Millar only selects 1assignment that he completed. Should he be surprised? To find out, we want to design a simulation to estimate the probability that Mr. Millar will randomly select 1or fewer of the homework assignments that Marino completed.

Get 30identical slips of paper. Write "N" on 10 of the slips and "C" on the remaining 20slips. Put the slips into a hat and mix well. Draw 1slip without looking to represent the first randomly selected homework assignment, and record whether Marino completed it. Put the slip back into the hat, mix again, and draw another slip representing the second randomly selected assignment. Record whether Marino completed this assignment. Repeat this process two more times for the third and fourth randomly selected homework assignments. Record the number out of the 4randomly selected homework assignments that Marino completed in this trial of the simulation. Perform many trials. Find the proportion of trials in which Mr. Millar randomly selects 1or fewer of the homework assignments that Marino completed.

Bull鈥檚-eye! In a certain archery competition, each player continues to shoot until he or she misses the center of the target twice. Quinn is one of the archers in this competition. Based on past experience, she has a 0.60probability of hitting the center of the target on each shot. We want to design a simulation to estimate the probability that Quinn stays in the competition for at least 10shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.

a. Slips of paper

b. Random digits table

c. Random number generator

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.

Mystery box Ms. Tyson keeps a Mystery Box in her classroom. If a student meets expectations for behavior, she or he is allowed to draw a slip of paper without looking. The slips are all of equal size, are well mixed, and have the name of a prize written on them. One of the 鈥減rizes鈥濃�攅xtra homework鈥攊sn鈥檛 very desirable! Here is the probability model for the prizes a student can win:

a. Explain why this is a valid probability model.

b. Find the probability that a student does not win extra homework.

c. What鈥檚 the probability that a student wins candy or a homework pass?
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