Franklin High School wanted to see if more boys than girls participated in school sports.
2.5.1 Practice: Assignment
Answer the following questions using what you’ve learned from this unit. Write your responses in the space provided.
Scoring: Each correct answer is worth 1 point. Where calculations are needed to find the answer, you must show your work to receive credit.
For questions 1 – 7, use the data in the table to answer the probability questions.
Franklin High School wanted to see if more boys than girls participated in school sports. A random survey of high school students was conducted, and the results are shown below:
NUMBER OF STUDENTS
| Participate in school sports | Do not participate in school sports | Totals | |
|---|---|---|---|
| Male | 110 | 180 | 290 |
| Female | 100 | 110 | 210 |
| Total | 210 | 290 | 500 |
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1. If a student is chosen at random from those who participated in the survey, what is the probability that the student is a male? Answer choices: 0.29 |
2. If a student is chosen at random from those who participated in the survey, what is the probability that the student is a male and participates in school sports? Answer choices: 0.22 |
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3. If a student is chosen at random from those who participated in the survey, what is the probability that the student participates in sports? Answer choices: 0.379 |
4. If a student is chosen at random from those who participated in the survey, what is the probability that the student participates in school sports, given that the student is a male? Answer choices: 0.379 |
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5. If a student is chosen at random from those who participated in the survey, what is the probability that the student is male, given that the student participates in sports? Answer choices: 0.379 |
6. To determine whether participating in sports and being male are independent events, which of the given probabilities should you compare? Select two choices. Answer choices: P(participate in sports) |
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7. Are participating in sports and being male independent events? Answer choices: Yes. The probabilities are the same. |
For questions 8 – 10, use the data in the table to answer the probability questions.
A swim coach is deciding which of five swimmers she should put in the free relay at the championship meet, and who should anchor. Each swimmer’s best time for 50 yards is between 29 and 30 seconds. To decide, the coach compares how many competitive swims were under 30 seconds. The swimmer who is least likely to swim under 30 seconds will be the alternate, and the swimmer most likely to swim under 30 seconds will be the anchor.
| Regular Season | ||
|---|---|---|
| Number of swims under 30 seconds | Total number of swims | |
| Carson | 6 | 9 |
| Ellis | 10 | 12 |
| Prestin | 8 | 11 |
| Ryan | 7 | 10 |
| Zach | 10 | 13 |
8. Complete the table to identify the probability that each swimmer can swim 50 yards in under 30 seconds during a regular season meet. Enter probabilities as decimals, rounded to two decimal places.
| Probability of swimming 50 yards in under 30 seconds | |
|---|---|
| Carson | |
| Ellis | |
| Prestin | |
| Ryan | |
| Zach |
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9. Which swimmer should the coach choose as alternate? Answer choices: Carson |
10. Which swimmer should the coach choose as anchor? Answer choices: Carson |
For questions 11 – 13, use the data in the table to answer the probability questions.
Jean is going to pick up treats for a meeting. To make sure she gets back in time, she plans to choose the store that is most likely to have parking nearby and short lines. She estimates the probability of these for two nearby stores. Assume available parking and line lengths are independent.
| Store A | Store B | |
|---|---|---|
| Probability of getting a close parking space | 0.9 | 0.8 |
| Probability that lines are short | 0.75 | 0.95 |
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11. What is the probability that Jean will find a close parking space and short lines at store A? Answer choices: 0.675 |
12. What is the probability that Jean will find a close parking space and short lines at store B? Answer choices: 0.675 |
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13. Which store should Jean choose to maximize the probability of finding a nearby parking space and getting in a short line? Answer choices: Store A |
For questions 14 – 15, identify the probability for each random number assignment.
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14. In a randomly generated list of numbers from 0 to 8, what is the probability that each number will occur? Answer choices: frac{1}{7}71 |
15. A randomly generated list of numbers from 0 to 7 is being used to simulate an event, with the numbers 0 and 1 representing a success. What is the estimated probability of a success? Answer choices: 20% |
For questions 16 – 20, use the random numbers given and the information in the question to assign numbers and estimate the probability of there being at least one left-handed person in a group of five people.
| 62349 | 02440 | 21460 | 70943 | 17506 | 94266 | 25109 | 01274 | 33656 | 11675 | ||||||||||
| 39380 | 36947 | 69235 | 93654 | 36711 | 27048 | 79415 | 16204 | 51022 | 27850 |
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16. About 10 percent of people are left-handed. Using single digits, which would be a correct method of assigning digits? Answer choices: Left-handed: 1; right-handed: 2 – 9 |
17. How many trials were included in the simulation? Answer choices: 5 |
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18. Using 0 to represent a left-handed person, how many trials included at least one left-handed person? Answer choices: 5 |
19. What is the estimated probability that there is at least one left-handed person in a group of five people? Answer choices: 11% |
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20. If you want to increase the likelihood that your estimated probability is close to the actual probability, what should you do? Answer choices: Change the assignment of digits. Increase the number of trials from 20 to 50. Decrease the number of trials from 20 to 10. Decrease the size of the random number groups from five digits to two. |
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