1.) In a study of 235 adults, the average heart rate was 82 beats per minute. Assume the population of heart rates is known to be approximately normal, with a standard deviation of 5 beats per minute. What does a margin of error of 0.8 for the 98% confidence interval of the average beats per minute mean?

A.) There is a 2% chance that the population mean is less than 82 beats per minute. B.) There is a 2% chance that the population mean is more than 82 beats per minute. C.) There is a 98% chance that the population mean is between between 77 and 87 beats per minute. D.) There is a 98% chance that the population mean is between 81.2 and 82.8 beats per minute. 2.) Nanna's Italian Restaurant has collected data about customer sauce orders. It calculated that P(marinara) = 0.64, P(alfredo) = 0.56, and P(marinara or alfredo) = 0.89. Determine the P(marinara and alfredo).

A.) 0.33 B.) 0.60 C.) 0.31 D.) 0.68 3.) The grades on the last math exam had a mean of 72%. Assume the population of grades on math exams is known to be distributed normally, with a standard deviation of 5%. Using the empirical rule, approximately what percent of students earned a score between 72% and 87%?

A.) 49.7% B.) 99.7% C.) 0.3% D.) 0.15% 4.) Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made?

A.) He did not use a random sample, and he tried to show cause and effect with an observational study. B.) He did not use a random sample, and he tried to show cause and effect with an experiment. C.) He did not separate his friends into different groups, and he didn't apply a treatment. D.) He did not separate his friends into different groups, and he used a survey to collect data. 5.) 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?

A.) Some customers who rate their service as high quality return for additional services. B.) Most customers who rate their service as high quality return for additional services. C.) High quality services cause customers to return for additional services. D.) Customers who will return for additional services report a high quality of service. 6.) 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?

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0Male Female Total Income over $50,000 475 375 850 Income below $50,000 75 75 150 Total 550 450 1,000