# Mathematics

Mathematics

Statistics for Decision Making final exam

1. Question:

(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.

Your Answer:

97,100

88,300

56,700

92,800

(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:

Your Answer:

This is an example of a Poisson probability experiment

This is an example of a Binomial probability experiment

This is neither a Poisson nor a Binomial probability experiment

Not enough information to determine the type of experiment

6 3. Question:

(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.

Your Answer:

0.131836

0.032959

0.004639

0.164795

(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?

Your Answer:

0.073263

0.146525

0.219788

0.219788

(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?

Your Answer:

Half the players are taller than 68 inches while half are shorter

The average height of the players on the team is 68 inches

More players are 68 inches tall than any other height.

The height of all the players is not very consistent because 68 is such a large number

Question:

(TCO 6) Using the standard normal distribution, find the probability that z is greater than 1.78

Your Answer:

0.0384

0.9625

0.9319

0.0375

(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.

Your Answer:

Reject the null hypothesis; there is enough evidence to reject the claim that the mean age of bus drivers in Denver is 56.9 years.

Reject the null hypothesis; there is enough evidence to support the claim that the mean age of bus drivers in Denver is 56.9 years.

Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean age of bus drivers in Denver is 56.9 years.

Fail to reject the null hypothesis; there not is enough evidence to support the claim that the mean age of bus drivers in Denver is 56.9 years.

(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.

Your Answer:

Fail to reject the null hypothesis; there is not enough evidence to reject the claim that less than 82% of health professionals would choose the same career.

Fail to reject the null hypothesis; there is not enough evidence to support the claim that less than 82% of health professionals would choose the same career.

Reject the null hypothesis; there is enough evidence to reject the claim that less than 82% of health professionals would choose the same career.

Reject the null hypothesis; there is enough evidence to support the claim that less than 82% of health professionals would choose the same career.

(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?

Your Answer:

Professor A because he got more consistent scores on his evaluation

Professor B because he got more consistent scores on his evaluation

Either professor because their average scores were the same

Neither professor because the given information is not enough to make a decision

10. Question:

(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.

Your Answer:

Expected profit from 10 customers = $3,650

Expected profit from 10 customers = $9,475

Expected profit from 10 customers = $9,125

Expected profit from 10 customers = $6,250

(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.

Your Answer:

The data is symmetric

The data is skewed to the right

The data is skewed to the left

The data is bimodal

(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?

Your Answer:

The sample size remains unchanged

The sample size needs to increase

The sample size needs to decrease

Not enough information is provided to draw a conclusion regarding the sample size in this case.

(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?

Your Answer:

85

92

90

93

(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?

Your Answer:

6545

658008

9880

105

(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?

Your Answer:

0.2119

1.00

0.8413

0.1587

(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).

Your Answer:

868.58

24122.9

23531.2

4495

(TCO 9) Describe the correlation in this graph.

Your Answer:

moderate positive

strong negative

moderate negative

strong positive

1. Question:

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

The mean life of a car’s engine is no more than 10 years.

(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. Question:

(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.

(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.

(a) Find the probability that the family’s monthly gasoline purchases will be between 86 and 96 gallons.

(b) Find the probability that the family’s monthly gasoline purchases will be less than 87 gallons.

(c) Find the probability that the family’s monthly gasoline purchases will be more than 75 gallons.

(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.

(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.

(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.

(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?