1. A stat teacher found that the actual time studying for the last test was normally distributed with a mean of 7.8 hours and a standard deviation of 1.7 hours. The teacher is concerned about the progress of the students in the lowest 5% of these times and wants to develop a study plan. What is the study time she should be looking for as the cut-off? (3pts) 2. The lengths of a comedy show at a local club are normally distributed with a mean of 62 minutes and a standard deviation of 20.5 minutes. a. What is the likelihood a randomly selected show lasted over 70 minutes? (3pts) b. You randomly select 16 performances. What is the probability their mean length is over 70 minutes? (4pts) c. Compare your answer from part a. and b. What accounts for any differences? You may draw a graph if that helps. (2pts)

Page 2 of 4 3. Among college students, the average weekly salary for those who work in a work study program is $270 with a standard deviation of $31. What is the probability that the mean salary for a sample of 40 students in the program is less than $260? (4pts) 4. The monthly utility bills in a certain city are normally distributed with a mean of $105 and a standard deviation of $12. a. Draw the distribution of monthly utility bills below, marking ,+, on the axis in the appropriate spots with the actual raw data values. (3pts) b. What's the likelihood a randomly chosen customer pays between $90 and $110? (3pts) c. Suppose the city wants to penalize the top 10% of utility users for using !too much"#electricity by assessing an extra fee. At what bill price do residents start getting hit with the penalty? (3pts)

Page 3 of 4 5. What happens to a confidence intervals' width when you increase the sample size but keep the level of confidence the same? (2pts) 6. In a random sample of 11 smartphones sold over the internet the mean sale price was $253. Assume the sale prices distribute approximately normally and the population standard deviation of the sale prices is $85. Find a 95% confidence interval for the mean sale price of all smartphones over the internet. Interpret your results. (5pts) 7. The National Center for Health Studies interviewed 5,409 adult smokers and found that 2,636 of them had attempted to quit smoking within the past year. Construct a 99% confidence interval for the proportion of adult smokers who attempted to quit smoking within the past year. Interpret your results. (5pts)

Page 4 of 4 8. Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. The Creel Survey reported that of a random sample of 51 fish caught, the mean length was 18.5 inches, with standard deviation 3.2 inches. Construct a 98% confidence interval for the mean length of fish in the lake. Interpret your results. (5pts) 9. The financial aid office at a local college needs information about student loans. They surveyed 16 randomly chosen students and collected some data. The mean loan amount for this sample was $2,286 with a standard deviation of $256. Assume the debt amounts are normally distributed. Find a 90% confidence interval for the population mean student debt. Interpret your results. (5pts) 10. An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 0.5 years of the population mean. Assume the population of ages is normally distributed. Determine the minimum required sample size to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 3.2 years. (3pts)