. Angelina’s Italian Restaurant has collected data about customer sauce orders. It calculated that P(pesto) = 0.42, P(alfredo) = 0.86, and P(pesto or alfredo) = 0.93. Determine the P(pesto and alfredo).

0.35

0.07

0.51

0.23

2. 

Brad is testing whether school is more enjoyable when students are making high grades. He asked 110 students if they enjoyed school and whether their GPA was above or below 3.5. He found that 38 of the 45 students with a GPA above 3.5 reported that they enjoyed school, and 7 of the 65 students with a GPA below 3.5 reported that they enjoyed school. What is the probability that a student with a GPA below 3.5 does not enjoy school?

89%

92%

85%

75%

3. In a study of 225 adults, the mean heart rate was 72 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute. What is the 90% confidence interval for the mean beats per minute?

70.7 – 73.3

70.9 – 73.1

70.7 – 73.1

70.9 – 73.3

4.A mechanic gives a survey to all of his customers asking them to rate the quality of the service they received. He then keeps track of how many customers return to the shop for additional services during the next six months. Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services. What conclusion can be drawn from this study?

Some customers who rate their service as high quality return for additional services.

Most customers who rate their service as high quality return for additional services.

High quality services cause customers to return for additional services.

Customers who will return for additional services report a high quality of service.

5. 

Amy is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is odd}, and let B = {the sum of the number cubes is divisible by 3}. List the outcomes in A ∪ B.

{3, 6, 9, 12}

{1, 3, 5, 7, 9, 11}

{3, 5, 6, 7, 9, 11, 12}

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

8. Lars wants to know if warming up will help runners sprint faster. Twenty-four track and field athletes volunteered to participate in his study. He randomly assigns 12 athletes to warm-up for 10 minutes. All 24 participants sprint the same distance. He calculates the mean for each group and determines that the mean for the warm-up group was 7.8 seconds and the mean for the other group was 9.8 seconds. To test the difference of means, he re-randomized the data 54 times and the differences are plotted in the dot plot below. What can Lars conclude from her study?



The difference in the means is significant because a difference of 2 is very likely.

The difference in the means is significant because a difference of 2 is not very likely.

The difference in the means is not significant because a difference of 2 is not very likely.

The difference in the means is not significant because a difference of 2 is very likely.

7.Hunter wants to prove to his parents that playing computer games while he studies for tests will help him get better grades. He decides to ask 30 of his friends if they play computer games while they study for their tests and what their grades are. He finds that his friends who have high grades also play computer games while they do their homework. He tells his parents that he has proven that playing games while studying for tests will cause his grades to improve. What mistake has Hunter made?

He did not use a random sample, and he tried to show cause and effect with an experiment.

He did not use a random sample, and he tried to show cause and effect with an observational study.

He did not separate his friends into different groups, and he didn’t apply a treatment.

He did not separate his friends into different groups, and he used a survey to collect data.

8. A survey of 1,200 men and women asked, “Do you earn over $75,000 per year?” The table below shows the responses for males and females:


Based on these data, are “being female” and “earning over $75,000” independent events?

No, P(being female | the person earns over $75,000) = P(being female)

No, P(being female | the person earns over $75,000) ≠ P(being female)

Yes, P(being female | the person earns over $75,000) = P(being female)

Yes, P(being female | the person earns over $75,000) ≠ P(being female)

9. The grades on the last science exam had a mean of 89%. Assume the population of grades on science exams is known to be normally distributed with a standard deviation of 4. What percent of students earn a score between 75% and 92%?

0.6823

0.7576

0.7956

0.7731

 10. 

Tanya drives to work every day and passes two independently operated traffic lights. The probability that both lights are red is 0.55. The probability that the first light is red is 0.69. What is the probability that the second light is red, given that the first light is red?

0.83

0.75

0.80

0.73