Test 3 SU3 Math 131 Name: Test 3 Total Points: 53 INSTRUCTIONS: Show all your work and good luck. Use the Genius Scan app to scan your completed test, then submit the pdf under the Assignments tab in...

How much for all questions?


Test 3 SU3 Math 131 Name: Test 3 Total Points: 53 INSTRUCTIONS: Show all your work and good luck. Use the Genius Scan app to scan your completed test, then submit the pdf under the Assignments tab in Canvas by 11:59pm on Thursday, August 6th. Round all solutions to the hundredths place. You must use the techniques and notation used in the screencasts on Canvas to answer the questions.
 1. A stat teacher found that the actual time studying for the last test was normally distributed with a mean of 8.1 hours and a standard deviation of 2.2 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 is normally distributed with a mean of 72 minutes and a standard deviation of 22.8 minutes. 
 
 a. What is the likelihood that a randomly selected show lasted between 60 minutes and 80 minutes?     (4pts)
 
 
 
 
 
 
 
 
 
 b. You randomly select 32 performances. What is the probability that their mean is between 60 minutes      and 80 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 of 1 5 3. Among college students, the average weekly salary for those who work in a work study program is $243 with a standard deviation of $34. What is the probability that the mean salary for a sample of 40 students in the program is more than $250? (4pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4. The monthly utility bills in a certain city are normally distributed with a mean of $110 and a standard   deviation of $15. a. Draw an accurate sketch of the distribution of monthly utility bills. Be sure to label the mean, as well as           the points one and two standard deviations away from the mean. (3pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 b. What’s the likelihood a randomly chosen customer pays less than $95? (3pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Page of 2 5 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)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5. The U.S. President’s approval rating is at 42% with a margin of error of 5%. Assume the level of confidence for the poll is 95%. Explain precisely what this means statistically, referencing specific numbers. (2pts)
 
 
 
 
 
 
 
 
 
 
 
 6. In a random sample of 28 sports cars, the average annual fuel cost was $2,218 and the standard deviation was $523. Construct a 90% confidence interval for . Assume the annual fuel costs are normally distributed. Interpret your results. (5pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 µ Page of 3 5 7. The National Study of the Changing Work Force conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question “What does success mean to you?” 1392 responded, “Personal satisfaction from doing a good job.” Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 99% confidence interval for p. Interpret your results. (5pts) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 8. If you were to increase the level of confidence while keeping everything else the same, would a confidence interval shrink, get larger, or stay the same? Explain. (2pts)
 
 
 
 
 
 
 
 
 
 
 9. 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 of 3.2 inches. Construct a 99% confidence interval for the mean length of fish in the lake. Interpret your results. (5pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Page of 4 5 10. 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)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 11. An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 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 1.2 years. (3pts)
 
 
 
 
 Page of 5 5