7) A tax auditor selects every 1000th income tax return that is received.

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1 Redwood High School. Department of Mathematics Advanced Algebra Stats wkst #3. Hard Worker's name: Solve the problem. Round results to the nearest hundredth. 1) The mean of a set of data 1) is 4.95 and its standard deviation is Find the z score for a value of ) A department store, on average, has daily sales of $28, The standard deviation of sales is $1000. On Tuesday, the store sold $36, worth of goods. Find Tuesday's z score. Was Tuesday an unusually good day? Find the number of standard deviations from the mean. Round your answer to two decimal places. 3) The annual snowfall in a 3) town has a mean of 30 inches and a standard deviation of 10 inches. Last year there were 67 inches of snow. How many standard deviations from the mean is that? Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience. 4) 49, 34, and 48 students are 4) selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. 5) A sample consists of every 49th student from a group of 496 students. 6) A market researcher selects 500 drivers under 30 years of age and 500 drivers over 30 years of age. 2) 5) 6) 7) A tax auditor selects every 1000th income tax return that is received. Solve the problem. Round results to the nearest hundredth. 8) The mean of a set of data 8) is 1.07 and its standard deviation is Find the z score for a value of Find the number of standard deviations from the mean. Round your answer to two decimal places. 9) The annual snowfall in a 9) town has a mean of 39 inches and a standard deviation of 12 inches. Last year there were 61 inches of snow. How many standard deviations from the mean is that? 10) In one town, the number of pounds of sugar consumed per person per year has a mean of 5 pounds and a standard deviation of 1.6 pounds. Tyler consumed 11 pounds of sugar last year. How many standard deviations from the mean is that? 11) Mario's weekly poker winnings have a mean of $328 and a standard deviation of $52. Last week he won $194. How many standard deviations from the mean is that? 7) 10) 11) 1

2 12) The number of hours per day a college student spends on homework has a mean of 6 hours and a standard deviation of 0.5 hours. Yesterday she spent 2 hours on homework. How many standard deviations from the mean is that? Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than or greater than Round the z-score to the nearest tenth if necessary. 13) A test score of 84.6 on a 13) test having a mean of 71 and a standard deviation of 8. 14) A body temperature of 96.5 F given that human body temperatures have a mean of F and a standard deviation of ) 14) Solve the problem. 16) In a survey of 1000 Americans, 850 said that they own a cell phone. Assume that the survey was properly conducted and that the 1000 people surveyed represent an unbiased sample of the entire population. Compute a 95% confidence interval (expressed using percents) for this survey. 17) In a survey of 1000 Americans, 850 said that they own a cell phone. Assume that the survey was properly conducted and that the 1000 people surveyed represent an unbiased sample of the entire population. Compute a 99.7% confidence interval (expressed using percents) for this survey. 16) 17) Provide an appropriate response. 15) The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 1480 and the standard deviation was 304. The test scores of four students selected at random are 1930, 1340, 2150, and a) Find the z-scores that correspond to each value b) Determine whether any of the values are unusual. 15) As part of a statistics project, a 6th grade teacher brings to class a container with 300 red marbles and 500 white marbles which are thoroughly mixed. To figure out how many marbles in the container are red without actually counting them all, a student randomly draws 40 marbles from the Of the 40 marbles drawn, 16 are red. 18) The target population consists of 18) A) the 16 marbles drawn by the student. B) the 800 marbles in the C) the 300 red marbles in the D) the 40 marbles drawn by the student. 19) The N-value for this population is 19) A) 300. B) 40. C) 16. D)

3 20) The sample consists of 20) A) the 40 marbles drawn by the student. B) the 300 red marbles in the C) the 16 red marbles drawn by the student. D) the 800 marbles in the 21) The sampling proportion is 21) A) %. B) %. C) % D) 5%. 22) Suppose that the student is given the N-value. What is a reasonable estimate for the number of red marbles in the container? A) 480 B) 320 C) 107 D) ) Suppose that the student is given the N-value. What is a reasonable estimate for the number of white marbles in the container? A) 300 B) 320 C) 107 D) ) The sampling error is most likely a result of A) nonresponse bias. B) a confounding variable. C) sampling variability. D) sampling bias. 22) 23) 24) 25) The sampling method used in this example is called A) stratified sampling. B) random sampling, but not simple random sampling. C) quota sampling. D) simple random sampling. As part of a statistics project, a 6th grade teacher brings to class a container with 200 red marbles and 800 white marbles which are thoroughly mixed. To figure out how many marbles in the container are red without actually counting them all, a student randomly draws 150 marbles from the Of the 150 marbles drawn, 33 are red. 26) The target population consists of 26) A) the 33 marbles drawn by the student. B) the 200 red marbles in the C) the 150 marbles drawn by the student. D) the 1000 marbles in the 25) 27) The N-value for this population is 27) A) 150. B) C) 33. D) ) The sample consists of 28) A) the 1000 marbles in the B) the 200 red marbles in the C) the 33 red marbles drawn by the student. D) the 150 marbles drawn by the student. 29) The sampling proportion is 29) A) 75%. B) 22%. C) 25%. D) 15%. 3

4 30) Suppose that the student is given the N-value. What is a reasonable estimate for the number of red marbles in the container? A) 220 B) 33 C) 150 D) ) The sampling method used in this example is called A) stratified sampling. B) random sampling, but not simple random sampling. C) simple random sampling. D) quota sampling. Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean. 32) Test scores: n = 95, x = 96.0, = 7.2; 99% confidence 33) Test scores: n = 82, x = 58.4, = 7.5; 98% confidence 34) A random sample of 78 light bulbs had a mean life of x = 494 hours with a standard deviation of = 37 hours. Construct a 90% confidence interval for the mean life, µ, of all light bulbs of this type. 32) 33) 34) 30) 31) 36) A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 247 milligrams with = 15.3 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, µ, of all such eggs. 37) 40 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 22.2 pounds and a standard deviation of 2.3 pounds. What is the 95% confidence interval for the true mean weight, µ, of all packages received by the parcel service? 38) A group of 69 randomly selected students have a mean score of 23.3 with a standard deviation of 4.5 on a placement test. What is the 90% confidence interval for the mean score, µ, of all students taking the test? 36) 37) 38) 35) A random sample of 112 full-grown lobsters had a mean weight of 23 ounces and a standard deviation of 2.8 ounces. Construct a 98% confidence interval for the population mean µ. 35) 4

5 In order to determine how American undergraduate college students feel about eliminating spring break in order to finish spring term a week early, a survey was conducted. Two hundred undergraduate students from the University of Miami (FL) were interviewed. Both of the interviewers hired to conduct the survey were told to interview 25 freshmen, 25 sophomores, 25 juniors, and 25 seniors. Of the 200 students interviewed, 20% were in favor of the elimination of spring break, 70% were opposed, and 10% had no opinion. 39) The target population for this 39) survey is A) the 180 students that had an opinion. B) the 200 students that were interviewed. C) all American undergraduate college students. D) all undergraduates at the University of Miami. 40) The sample for this survey is 40) A) the 200 students that were interviewed. B) all undergraduates at the University of Miami. C) the 180 students that had an opinion. D) all American undergraduate college students. 41) Based on the fact that 20% of the students interviewed were in favor of the elimination of spring break, the value 20% is A) a population. B) a statistic. C) a sample. D) a parameter. 41) 42) Which of the following best describes the parameter in this situation? A) The percentage of American college students that undergraduates at the Univeristy of Miami (FL) represent. B) The actual percentage of American college students that favor the elimination of spring break. C) The 20% of students interviewed that favored the elimination of spring break. D) The actual percentage of students at the University of Miami (FL) that favor the elimination of spring break. 43) The results of this survey are unreliable primarily because of A) both selection bias and non-response bias. B) selection bias only. C) the absence of a control group. D) nonresponse bias only. 44) The sampling proportion in this survey is A) 20%. B) 200/(the number of American college students). C) 100%. D) 200/(the number of University of Miami, FL undergraduates). 45) The sampling method used for the survey is called A) random sampling. B) simple random sampling. C) quota sampling. D) stratified sampling. 42) 43) 44) 45) 5

6 Use a z-table to determine the percent of data specified. 46) Between z = 1.41 and z = 46) ) Between z = 0.54 and z = ) Between z = and z = ) 48) 49) Greater than z = ) 50) Less than z = ) 56) Less than 690 hours 56) Solve the problem. 57) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? 57) A child has an enormous jar in which she has been saving all of her spare change. In order to determine exactly how much money she has in the jar, she dumps all of the coins on the floor and counts them. Under the watchful eye of her mother, she counts 180 pennies, 120 nickels, 100 dimes, and 80 quarters. 51) If the child were to grab a handful 51) of 48 coins at random from the jar, how much money should she expect it to be worth? A) $3.78 B) $39.60 C) $4.92 D) $ ) The data collection method used in this example is called A) a survey. B) random sampling. C) a controlled study. D) a census. A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the percentage of bulbs that can be expected to last the period of time. 53) At least 500 hours 53) 52) 58) The average size of the fish in a lake is 11.4 inches, with a standard deviation of 3.2 inches. Find the percentage of fish longer than 17 inches. 59) 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. If an applicant is randomly selected, find the percentage of applicants with a rating that is between 170 and ) 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. If an applicant is randomly selected, find the percentage of applicants with a rating that is between 200 and ) 59) 60) 54) Between 500 hours and 675 hours 54) 55) Between 290 hours and 540 hours 55) 6

7 61) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours. 61) 62) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours. 62) 63) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than ) 64) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than ) 7

8 Answer Key Testname: H ADVALG S2 TEST 8 STATS WKSV 3 1) ) 8.12, yes 3) 3.70 standard deviations above the mean 4) Stratified 5) Systematic 6) Stratified 7) Systematic 8) ) 1.83 standard deviations above the mean 10) 3.75 standard deviations above the mean 11) 2.58 standard deviations below the mean 12) 8.00 standard deviations below the mean 13) 1.7; not unusual 14) -2.7; unusual 15) a) x = 1930 z 1.48 x = 1340 z x = 2150 z 2.20 x = 1450 z b) x = 2150 is unusual because its corresponding z-score (2.20) lies more than 2 standard deviations from the mean. 16) 82.8% to 87.2% 17) 81.7% to 88.3% 18) B 19) D 20) A 21) D 22) B 23) D 24) C 25) D 26) D 27) B 28) D 29) D 30) A 31) C 32) 94.1 < µ < ) 56.5 < µ < ) 487 hr < µ < 501 hr 35) 22 oz < µ < 24 oz 36) 244 mg < µ < 250 mg 37) 21.5 lb < µ < 22.9 lb 38) 22.4 < µ < ) C 40) A 41) B 42) B 43) B 44) B 45) C 46) 7.70% 8

9 Answer Key Testname: H ADVALG S2 TEST 8 STATS WKSV 3 47) 26.65% 48) 90.70% 49) 96.56% 50) 83.40% 51) A 52) D 53) 50% 54) 46% 55) 63.8% 56) 97.1% 57) 1.96% 58) 4.01% 59) 38.11% 60) 43.32% 61) ) ) )