# MATH 221 Week 8 Final Exam

**MATH 221 Final Exam**

- (TCO 9) The annual Salary of an electrical engineer is given in terms of the years of experience by the table below. Find the equation of linear regression for the above data and obtain the expected salary for an engineer with 45 years of experience. Round to the nearest $100.
- (TCO 5) A company produces window frames. Based on a statistical analysis, we found that 15% of their product is defective. They have shipped 10 windows to one of their customers. The customer is worried about the probability of having defective frames. Choose the best answer of the following:
- (TCO 5) A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly.
- (TCO 5) It has been recorded that the average number of errors in a newspaper is 4 mistakes per page. What is the probability of having 1 or 2 errors per page?
- (TCO 2) The median height of the players on a high school basketball team is 68 inches. What does this tell you about the typical height of a player on this team?
- (TCO 6) Using the standard normal distribution, find the probability that z is greater than 1.78
- (TCO 8) The mean age of school bus drivers in Denver is claimed to be 56.9 years. A hypothesis test is performed at a level of significance of 0.01 with a P-value of 0.09. Choose the best interpretation of the hypothesis test.

8.(TCO 8) A poll of U.S. health professionals revealed less than 82% would choose the same career. In a hypothesis test conducted at a level of significance of 1%, a P-value of 0.035 was obtained. Choose the best interpretation of the hypothesis test.

9.(TCO 2) You are going to take a statistics class next session. You have two professors to choose from. Both professors have a mean performance evaluation score of 3.56 out of 4. Professor A has a standard deviation of .86 while Professor B has a standard deviation of .51. You want to choose the better professor because math is a challenge for you, who do you choose?

10.(TCO 4) A travel agency offers 4 different vacation packages to Europe. Their net profit for package 1 is $500, for package 2 it is $750, for package 3 it is $900, and for package 4 it is $1,500. From past experience they know that 20% of their customers purchase package 1, 15% of their customers purchase package 2, 40% of their customers purchase package 3 and 25% of their customers purchase package 4. Find the expected value or average profit per customer and determine how much profit they should expect if 10 people purchase one of their European vacation packages.

11.(TCO 3) The ages of 25 employees in a company are listed below: Use the stem & leaf plot to determine the shape of the distribution. Choose the best answer.

12.(TCO 1) A statistician is considering using a 99% confidence interval for a study instead of a 95% confidence interval. What happens to the required sample size if the confidence level is increased from 95% to 99% and the same error is required in each case?

13.(TCO 6) Scores on an assessment exam at a private school are normally distributed, with a mean of 75 and a standard deviation of 11. Any student who scores in the top 7% is eligible for a scholarship. What is the lowest whole number score you can earn and still be eligible for a scholarship?

14.(TCO 5) A shipment of 40 computers contains five that are defective. How many ways can a small business buy three of these computers and receive no defective ones?

- (TCO 6) The time required to make 1100 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 16 hours and a standard deviation of 3 hours. What is the probability that it will take more than 19 hours to make 1100 gallons of synthetic rubber?

16.(TCO 10) The annual rice yield (in pounds), is given by the equation y-hat = 859 + 5.76a + 3.82b, where ‘a’ is the number of acres planted (in thousands), and ‘b’ is the number of acres harvested (in thousands). Predict the annual rice yield (in pounds) when the number of acres planted is 2550 (in thousands) and the number of acres harvested is 2245 (in thousands).

- (TCO 9) Describe the correlation in this graph.

**Page 2**

1.(TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.

2.(TCO 11) A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 35 service times was collected, and the sample mean was found to be 16.2 minutes, with a sample standard deviation of 3.5 minutes. Is there evidence to support, or to reject the claim at the alpha = 0.05 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. Writing the formal conclusion is an important part of the process.

3.(TCO 5) The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized? (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability that, out of 50 houses, exactly 4 of the houses will be burglarized. Show your calculations or explain how you found the probability.

4.(TCO 6) The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random.

5.(TCO 8) An engineering firm is evaluating their back charges. They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.04, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.

6.(TCO 7) A marketing firm wants to estimate the average amount spent by patients at the hospital pharmacy. For a sample of 200 randomly selected patients, the mean amount spent was $92.75 and the standard deviation $13.10. (a) Find a 95% confidence interval for the mean amount spent by patients at the pharmacy. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.

7.(TCO 7) A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 15 people with the condition currently untreated. From this small sample, the mean heart rate is 92 beats per minute with a standard deviation of 8. (a) Find a 98% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.

8.(TCO 2) The heights of 10 sixth graders are listed in inches: {50, 62, 54, 57, 60, 57, 53, 57, 59, 58}. (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?