AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Introduction to Probability

Introduction to Probability Answers

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Dropping a piece of buttered toast will theoretically land butter-side down with a probability of 0.65. Some students decided to test this theory and dropped five pieces of buttered toast. All five landed butter-side down. One of the students claims that the next piece of buttered toast dropped will land butter-side up because it is due to happen.

A
Yes, the students need to start dropping buttered toast to land butter up to get back to 0.65.
B
No, the probability of buttered toast landing butter-side down is 0.65 over a large number of trials.
C
No, if buttered toast lands butter-side down five times in a row, the probability must be higher than 0.65.
D
Yes, it is unlikely that five pieces of dropped buttered toast will land butter-side down, so butter up must be due.
2
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An online news report claims that 50% of online news readers work in the business industry. To test this claim, a researcher takes an SRS of 25 online news readers. Nine of them work in the business industry. A simulation of 65 trials was conducted under the assumption that 50% of online news readers really do work in the business industry.

Question illustration
A
Since 0.36 of the sample works in the business industry, 0.36 is the true probability that an online news reader works in the business industry.
B
It is most likely that, out of 25 online readers, between 12 and 13 work in the business industry.
C
Because there appear to be outliers present that are greater than 16, we can conclude that more than 50% of online readers work in the business industry.
D
There is about a 0.046 chance that 9 or fewer online readers work in the business industry. This is unusual and is convincing evidence that less than 50% of online readers work in the business industry.
3

Carlos thinks the traffic light to get out of his neighborhood is red more often than green. He decides to collect data to determine the probability of the light being red upon his approach. The graph of his long-run relative frequencies is shown.

Question illustration
A
About half of the time, the traffic light is red when Carlos leaves his neighborhood.
B
About 63% of the time, the traffic light is red when Carlos leaves his neighborhood.
C
If the true probability that the traffic light is red when Carlos leaves his neighborhood is 0.63, there would be no variation in the graph.
D
The probability that the traffic light is red when Carlos leaves his neighborhood cannot be determined from this graph because there is no pattern in a long series of traffic lights.
4

A local restaurant is having a contest in which patrons spin a wheel to win prizes. The wheel is divided into 10 identical segments, each marked with a different prize. Seven of the segments are labeled "Free Entrée” or "Free Appetizer.” The other three are labeled "Free Valet Parking.”Let the digits 0–6 represent winning free food and 7–9 represent winning valet parking.

Question illustration
A
5
B
10
C
12
D
15
5

A fitness expert claims that 25% of adults do not know how to swim. To test this claim, an SRS of 20 adults is taken. Two of the adults do not know how to swim. A simulation of 100 trials is conducted based on the assumption that 25% is the true probability that an adult does not know how to swim.

Question illustration
A
The actual probability that an adult cannot swim is only 12%.
B
It is clear that exactly 5 out of 20 adults will be nonswimmers.
C
If we continued to take more samples of 10 adults, the center of the distribution would shift to 2.
D
There is about a 12% chance of 2 or fewer nonswimmers in a group of 20. This is not unusual and is not convincing evidence that the true probability that an adult cannot swim is less than 25%.
6

About 20% of the population experiences "cybersickness.” This happens when the images in 3-D movies look so real they hinder the brain’s ability to sort signals and cause people to get nauseated. To find out if this applies to teens, an SRS of 30 high school students was asked if they experience cybersickness. Eight students said "Yes.” To see if this result is surprising, a simulation is conducted to estimate the probability of obtaining a sample result as high as this.Let 0–1 represent "Yes” and 2–9 represent "No.” Using the line of random numbers, how many "Yes” responses will there be in the first trial of the simulation?

Question illustration
A
2
B
4
C
15
D
26
7

A contractor claims that she finishes a job on time 90% of the time. Last month, she only completed 7 out of her 10 jobs on time. To see if this is surprisingly low, a simulation was conducted 100 times under the assumption that she really does complete 90% of her jobs on time. The dotplot contains 100 trials of this simulation.

Question illustration
A
The contractor’s true, on-time completion rate is only 50%.
B
It is most likely that the contractor will complete about 9 out of 10 jobs.
C
If we used a larger sample size of 40 jobs, the simulated dotplot would be different; therefore, we cannot draw a conclusion.
D
The dotplot does not provide convincing evidence that her true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.
8

A study reports that about half of pet owners have either a dog or a cat. The other half of pet owners have birds, reptiles, or other animals. To find out if this applies in its area, an animal shelter surveys a random sample of 30 pet owners. Nineteen of them say they own either a cat or a dog.Let even digits represent owning a cat or a dog and odd digits represent owning some other type of animal.Using the line of random numbers, what is the best estimate of the proportion of responses in a sample who own either a cat or a dog?

Question illustration
A
0.47
B
0.50
C
0.53
D
0.63
9

A study reported that about half of high school seniors study for upcoming math tests. To find out if this applies to seniors at Garfield High School, an SRS of 30 seniors was asked if they study for their math tests. Nineteen responded "Yes.”A dotplot is provided showing the results of 40 trials of this simulation.

Question illustration
A
No, there is an outlier at 20.
B
No, there were outcomes as low as 12.
C
Yes, only one trial had a result of 19 or larger.
D
Yes, more than half of the simulated results are over 15.
10

A teacher claims that there is a 50% chance that she will collect homework for a grade on any given day. One week, she collected all five daily homework assignments. A student in this class is upset and explains that the teacher should not collect any homework assignments the following week in order to honor her 50% probability claim.

A
Yes, the teacher should not collect homework assignments next week to bring the probability of homework being collected back to 0.5.
B
No, if the teacher collects homework five days in a row, it is not possible for the probability of homework being collected to be 0.5.
C
Yes, it is unlikely that the teacher would randomly collect homework assignments five days in a row, so not having a homework collection next week is due to happen.
D
No, collecting homework and not collecting homework are equally likely in the long run, so whether or not the teacher collects homework on any single day cannot be determined.

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