problems
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problems

Course Number: MATH 221, Spring 2011

College/University: DePaul

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Page 1 1.(TCO 9) The hours of study and the final exam grades have this type of relationship: = 5.76(hours) + 35.31. Based on this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your answer to two decimal places. (Points:6) 46.08 81.39 91.45 85.29 2.(TCO 5) At a drive through window of a bank its found that 10 customers get served every 15 minutes. The...

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1 1.(TCO Page 9) The hours of study and the final exam grades have this type of relationship: = 5.76(hours) + 35.31. Based on this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your answer to two decimal places. (Points:6) 46.08 81.39 91.45 85.29 2.(TCO 5) At a drive through window of a bank its found that 10 customers get served every 15 minutes. The banks manage is interested in finding a way to increase the number of customers that can be served. He thought that knowing the probability of serving 12 customers per 15 minutes could be helpful to him in the decision making process. Choose the best answer of the following: (Points:6) 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 3.(TCO 5) Microfracture knee surgery has a 75% chance of success on patients with degenerative knees. The surgery is performed on 5 patients. Find the probability of the surgery being successful on 3 or 4 patients?(Points:6) 0.103516 0.659180 0.762695 0.642875 4.(TCO 5) It has been recorded that 10 people get killed by shark attack every year. What is the probability of having 5 or 6 people get killed by shark attack this year? (Points:6) 0.130141 0.026484 0.100889 0.067086 5.(TCO 2) The median teaching hours for a full time faculty at a state university is eight hours per week. What does this tell you about the typical teaching hours for full time faculty at that university? (Points:6) Half of the full time faculties teach less than eight hours per week while half teaches more than eight hours per week. The average teaching hours for full time faculty is eight hours per week. More full time faculty teaches eight hours per week than any other number of teaching hours. The number of teaching hours for full time faculty in not very consistent because eight is such a low number. 6.(TCO 6) Assuming that the data are normally distributed with a mean of 15 and a standard deviation of 1.5, what is the z-score for a value of 13?(Points:6) -1.33 -2.10 1.33 1.49 7.(TCO 8) The mean hours of Internet usage by adults in the US in claimed to be 25 hours per week. A hypothesis test is performed at a level of significance of 0.05 with a P-value of 0.08. Choose the best interpretation of the hypothesis test.(Points:6) Reject the null hypothesis; there is enough evidence to reject the claim that the mean of hours Internet usage by adults in the US is 25 hours per week. Reject the null hypothesis; there is enough evidence to support the claim that the mean hours Internet usage by adults in the US is 25 hours per week. Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean hours of Internet usage by adults in the US is 25 hours per week. Fail to reject the null hypothesis; there is not enough evidence to support the claim that the mean hours of Internet usage by adults in the US is 25 hours per week. 8.(TCO 8) A result of an entry level exam reveals that more than 22% of students fail that exam. In a hypothesis test conducted at a level of significance of 2%, a P-value of 0.035 was obtained. Choose the best interpretation of the hypothesis test.(Points:6) Fail to reject the null hypothesis; there is not enough evidence to reject the claim that 22% of students fail the entry level exam. Fail to reject the null hypothesis; there is not enough evidence to support the claim that 22% of students fail the entry level exam. Reject the null hypothesis; there is enough evidence to reject the claim that 22% of students fail the entry level exam. Reject the null hypothesis; there is enough evidence to support the claim that 22% of students fail the entry level exam. 9.(TCO 2) You want to buy light bulbs and you want to choose between two vendors. Vendor As light bulbs have a mean life time of 800 hours and a standard deviation of 175 hours. Vendor Bs light bulbs also have a mean life time of 800 hours, but a standard deviation of 225 hours. You want light bulbs that have more life time consistency, which vendor will you purchase from? (Points:6) Vendor A because you will be more likely get light bulbs with the same life time Vendor B because you will be more likely get light bulbs with the same life time Either one because both produce light bulbs with the same mean life time. Neither one because a mean height of 800 inches is too short for a light bulb. 10.(TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 45% red, 35% blue, 15% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $5, $15, $25, $60 for red, blue, yellow and green ball respectively. Winning amount 5 15 25 60 Probability 45 % 35 % 15 % 5% (Points:6) The expected The expected The expected The amount expected winning is $28.50 winning amount is $14.25 winning amount is $25.50 winning amount is $11.25 11.(TCO 3) The grades of 20 students are listed in the stem and leaf diagram below. What is the probability of randomly selected student to have a grade more than or equal to 60 and less than or equal to 80. 4|4 5|68 6|579 7|157889 8|0257889 9|7 (Points:6) 0.65 0.50 0.45 -0.55 12.(TCO 1) A researcher is interested in studying peoples mean age in a certain region. If the population standard deviation is known to be 8 years and 1.5 year of error margin is allowed, find the minimum simple size the researcher needs to use, knowing that he is going to conduct his study using 95% confidence level.(Points:6) Sample Size = 77 Sample Size = 25 Sample Size = 210 Sample Size = 110 13.(TCO 6) Horse race time is found to be normally distributed with a mean value of 10 minutes and a standard deviation of 2 minutes. Horses whose race time is in the top 5% will not be eligible to participate in a second round. What is the lowers race time that makes a horse losses his eligibility to participate in a second round? (Points:6) 13.29 12 6.71 15.29 14.(TCO 5) A class containing 15 students 5 of them are females. In how many ways can we select a group of 4 male students?(Points:6) 260 120 5040 210 15.(TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 60,000 miles and a standard deviation of 5,000 miles. What is the probability of having a tire that lasts more than 67,000 miles?(Points:6) 0.9192 0.0808 1.40 0.0793 16.(TCO 10) A research shows that employee salaries at company XYX, in thousands of dollars, are given by the equation y-hat= 48.5 + 2.2 a + 1.5 b where a is the years of experience, and b is the education level in years. In thousands of dollars, predict the salary for an employee with 10 years experience and 14 years education level.(Points:6) 52.2 72.5 70.5 91.5 17.(TCO 9) The estimated value for the correlation coefficient for this graph might be (Points:6) -0.91 0.50 0.91 -0.50 Page 2 1.(TCO8)Forthefollowingstatement,writethenullhypothesisandthealternativehypothesis.Alsolabel whichoneistheclaim. CompanyXclaimsthattheaveragesalaryforanentrylevelemployeeis$35,000 (Points:8) 2.(TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the managers claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points:20) 3.(TCO 5) A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions correctly. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions. Show your calculations or explain how you found the probability. (Points:20) 4.(TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20. (a) Find the probability of having a utility bill between 135 and 170. (b) Find the probability of having a utility bill less than $135. (c) Find the probability of having a utility bill more than $180. (Points:20) 5.(TCO 8) A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. At alpha = 0.05, test the Malls manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.(Points:20) 6.(TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 50 businesses, he found the mean number of transaction per month to be 35 and the standard deviation to be 9.5 transactions. (a) Find a 99% confidence interval for the mean number of business transactions per month. 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. (Points:20) 7.(TCO 7) A companys CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 400 products, he found 25 defective products. (a) Find a 95% confidence interval for the true proportion of defective product. 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. (Points:20) 8.(TCO 2) The ages of 10 students are listed in years:{ 17,22,19,24,21,23,29,18,22,28 } (Points:20)

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