MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Sample Final Exam Spring 2008 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion. 1) Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community. A) (3.30%, 9.17%) B) (4.16%, 8.30%) C) (5.32%, 7.14%) D) (2.99%, 9.47%) E) (3.77%, 8.70%) 1) Construct the requested confidence interval from the supplied information. 2) A sample of 81 statistics students at a small college had a mean mathematics ACT score of 26 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all statistics students at this college. A) (25.3, 26.7) B) (25.9, 26.1) C) (24.7, 27.3) D) (78.6, 83.4) E) (25.3, 26.1) Interpret the confidence interval. 3) Analysis of a random sample of 250 Illinois nurses produced a 95% confidence interval for the mean annual salary of $42,838 < m(nurse Salary) < $49,691. A) We are 95% confident that the average nurse salary in the U.S. is between $42,838 and $49,691. B) If we took many random samples of Illinois nurses, about 95% of them would produce this confidence interval. C) About 95% of Illinois nurses earn between $42,838 and $49,691. D) About 95% of the nurses surveyed earn between $42,838 and $49,691. E) We are 95% confident that the interval from $42,838 to $49,691 contains the true mean salary of all Illinois nurses. Determine the margin of error in estimating the population parameter. 4) Based on a sample of size 49, a 95% confidence interval for the mean score of all students on an aptitude test is from 64.3 to A) 0.05 B) 5.4 C) 2.7 D) 0.76 E) Not enough information is given. 2) 3) 4) 1

2 Construct the indicated confidence interval for the difference between the two population means. Assume that the assumptions and conditions for inference have been met. 5) A grocery store is interested in determining whether or not a difference exists between the shelf life 5) of two different brands of doughnuts. A random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box. The sample results are given below. Brand A Brand B x = 2.1 x = 2.9 s = 0.8 s = 1.1 n = 100 n = 100 Find a 90% confidence interval for m A - m B, the difference in mean shelf life between brand A and brand B. A) (-1.03, -0.58) B) (0.08, 1.53) C) (0.58, 1.03) D) (2.1, 2.9) E) (-1.53, -0.08) Find the mean of the data. 6) Here are the grocery bills, in dollars, for six shoppers. 6) $46.70 $78.64 $71.05 $71.68 $50.71 $79.34 Round your answer to the nearest cent. A) $79.62 B) $67.62 C) $99.53 D) $66.35 E) $71.68 Find the median for the given sample data. 7) The distances traveled (in miles) to 7 different swim meets are given below: 22, 24, 39, 45, 65, 68, 84 Find the median distance traveled. A) 50 miles B) 45 miles C) 65 miles D) 39 miles 7) Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 8) 196, 205, 215, 185, 229, 278, 165 8) A) 33.1 B) 30.2 C) 12.7 D) 36.2 Find the number of standard deviations from the mean. Round to the nearest hundredths. 9) The weights of children age two average 25 pounds with a standard deviation of 3 pounds. How many standard deviations from the mean is a weight of 18 pounds? A) About 2.33 standard deviations below the mean B) About 1.22 standard deviations below the mean C) About 1.39 standard deviations above the mean D) About 2.33 standard deviations above the mean E) About 1.22 standard deviations above the mean 9) 2

3 Solve the problem. 10) A town's snowfall in December averages 19 inches with a standard deviation of 8 inches while in February, the average snowfall is 43 inches with a standard deviation of 14 inches. In which month is it more likely to snow 32 inches? Explain. A) December. Snowfall of 32 inches is from the mean while snowfall of 32 inches is from the mean in February. B) It is equally likely in either month. One can't predict Mother Nature. C) February. Snowfall of 32 inches is 13 8 the mean in December. from the mean while snowfall of 32 inches is from D) February. Snowfall of 32 inches is from the mean while snowfall of 32 inches is 14 8 from the mean in December. E) December. Snowfall of 32 inches is from the mean while snowfall of 32 inches is 14 8 from the mean in February. 11) A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what percentage can be expected to be between 200 and 275? A) 6.68% B) 42.37% C) 5.00% D) 93.32% E) 43.32% Find the indicated probability. 12) The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than inches? A) B) C) D) Solve the problem. 13) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%. A) B) C) D) Find the indicated probability. 14) A die with 12 sides is rolled. What is the probability of rolling a number less than 11? A) 1 B) 5 C) 10 D) ) 11) 12) 13) 14) 15) Of the 92 people who answered "yes" to a question, 5 were male. Of the 49 people that answered "no" to the question, 13 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? A) B) C) D) ) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. A) B) 2.1 C) D) ) 16) 3

4 17) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. 17) toppings freshman sophomore junior senior cheese meat veggie Among the juniors what is the probability that a student responded "meat"? A) B) C) D) 0.15 E) ) You are dealt a hand of three cards, one at a time. Find the probability that you have at least one face card. A) B) C) D) E) Find the expected value of the random variable. 19) The probability model below describes the number of thunderstorms that a certain town may experience during the month of August. 18) 19) Number of storms Probability How many storms can the town expect each August? A) 1.9 B) 1.8 C) 2.3 D) 1.5 E) 2.0 Find the indicated probability. 20) An archer is able to hit the bull's eye 76% of the time. If she shoots 10 arrows, what is the probability that her first bull's-eye comes on the 4th arrow? Assume each shot is independent of the others. A) 0.76 B) C) D) E) Solve. 21) Suppose that 12% of students at one college have high blood pressure. If you keep picking students at random from this college, how many students do you expect to test before finding one with high blood pressure? A) 12 B) 0.88 C) 1.14 D) 8.33 E) 0.12 Find the specified probability, from a table of Normal probabilities. 22) The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine puts in the boxes is believed to have a Normal model with mean ounces and standard deviation 0.3 ounces. What is the probability that the mean weight of a 16-box case of crackers is below 16 ounces? A) B) C) D) E) ) 21) 22) 4

5 Answer the question. 23) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of his or her tosses that were tails. The students then report their results, and the professor records the proportions. One student claims to have tossed her coin 200 times and found 60% tails. What do you think of this claim? Explain your response. A) This is a fairly unusual result. Her proportion is about 2.00 standard deviations above the mean. B) This is a fairly unusual result. Her proportion is about 2.83 standard deviations above the mean. C) This is a typical result. Her proportion is only 2.83 standard deviations above the mean. D) This is a typical result. Her proportion is only 2.00 standard deviations above the mean. E) This is an extremely unlikely result. Her proportion is about 200 standard deviations above the mean. Find the probability of the outcome described. 24) A beginning archer is able to hit the bull's-eye 39% of the time. If she shoots 9 arrows, what is the probability that she gets at most 3 bull's-eyes? Assume each shot is independent of the others. A) B) C) D) E) ) 24) 5

6 Answer Key Testname: SAMPLE FINAL 1) E 2) C 3) E 4) C 5) A 6) D 7) B 8) D 9) A 10) D 11) E 12) C 13) C 14) B 15) C 16) D 17) C 18) E 19) B 20) B 21) D 22) A 23) B 24) A 6