AP Statistics - Chapter 2

A

10. The mean time required to assemble an electronic component used in CD players is 12 minutes, and the standard deviation is 2.1 minutes. If the distribution is approximately normal, from this we can determine that at least ___% of the assembly times will be between 9.9 minutes and 14.1 minutes. a. 68 b. 75 c. 89 d. 94 e. 95

C

11. A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test? a. 82 b. 88 c. 100 d. 112 e. 118

B

2. A student discovers that his grade on a recent test was the 72nd percentile. If 90 students took the test, then approximately how many students received a higher grade than he did? a. 65 b. 25 c. 72 d. 71 e. 18

E

30. Heights of males are approximately normally distributed with a mean of 170 cm and a standard deviation of 8 cm. What fraction of males are taller than 176 cm? a. .7500 b. .6000 c. .2734 d. .2500 e. .2266

C

31. The height of an adult male is known to be normally distributed with mean of 175 cm and standard deviation 6 cm. The 20th percentile of the distribution of heights is: a. 175 b. 179 c. 170 d. 172 e. 174

B

32. The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might expect in a sample of 1000 students that the number with heights less than 163 cm is: a. 997 b. 23 c. 477 d. 228 e. 456

C

33. The height of an adult male is known to be normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. The height of the doorway such that 96 percent of the adult males can pass through it without having to bend is: a. 1.75 b. 64.63 c. 73.38 d. 79.94 e. 58.06

D

35. The distribution of weights of a large group of high school students is normally distributed with kg and kg. Which of the following is FALSE? a. About 16 percent of the students will be over 60 kg. b. About 2.5 percent will be below 45 kg. c. Half of them can be expected to weigh less than 55 kg. d. About 5 percent will weigh less than 63 kg. e. About 68% are between 50 and 60.

D

36. The daily milk production of Guernsey cows is approximately normally distributed with a mean of 35 kg/day and a std. deviation of 6 kg/day. The probability that a days production for a single animal will be less than 28 kg. is approximately: a. .41 b. .09 c. .38 d. .12 e. .62

D

37. Refer to the previous question. The producer is concerned when the milk production of a cow falls below the 5th percentile since the animal may be ill. The 5th percentile (in kg) of the daily milk production is approximately: a. 1.645 b. -1.645 c. 33.36 d. 25.13 e. 44.87

E

38. Which of the following is NOT CORRECT about a standard normal distribution? P(0 < Z < 1.50) = .4332 P(Z < -1.0) = .1587 P(Z > 2.0) = .0228 P(Z < 1.5) = .9332 P(Z > -2..5) = .4938

D

39. The value of such that P(Z < Z0) is a. 1.96 b. 1.645 c. 2.33 d. 1.28

B

7. The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to: a. 2 b. 3 c. 6 d. 9 e. 12

E

34. The distribution of weights in a large group is approximately normally distributed. The mean is 80 kg. and approximately 68% of the weights are between 70 and 90 kg. The standard deviation of the distribution of weights is equal to: a. 20 b. 5 c. 40 d. 50 e. 10

C

19. Refer to the previous question. Problem drinkers will be classified as those in the upper 10% of consumption. What is the approximate lower bound for the consumption of problem drinkers? a. 15 oz b. 18 oz c. 17 oz d. 10% e. 90%

C

1. Many professional schools require applicants to take a standardized test. Suppose that 1000 students took the test, and you find that your mark of 63 (out of 100) was the 73rd percentile. This means : a. At least 73% of the people got 63 or better. b. At least 270 people got 73 or better. c. At least 270 people got 63 or better. d. At least 27% of the people got 73 or worse. e. At least 730 people got 73 or better.

C

12. One of the side effects of flooding a lake in northern boreal forest areas (e.g. for a hydro-electric project) is that mercury is leached from the soil, enters the food chain, and eventually contaminates the fish. The concentration in fish will vary among individual fish because of differences in eating patterns, movements around the lake, etc. Suppose that the concentrations of mercury in individual fish follows an approximate normal distribution with a mean of 0.25 ppm and a standard deviation of 0.08 ppm. Fish are safe to eat if the mercury level is below 0.30 ppm. What proportion of fish are safe to eat? a. 23% b. 27% c. 37% d. 63% e. 73%

C

13. Refer to the previous question. The Department of Fisheries and Oceans wishes to know the mercury level of the top 20% of the fish. The appropriate percentile and mercury level for this lake is: a. 20th percentile has a value of -0.84 ppm b. 20th percentile has a value of 0.18 ppm c. 80th percentile has a value of 0.32 ppm d. 80th percentile has a value of 0.84 ppm e. 20th percentile has a value of 0.07 ppm

A

14. Marks on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximately what percentage of the students have scores below 50? a. 11% b. 89% c. 15% d. 18% e. 39%

A

15. Refer to the preceding question. What is the approximate 90th percentile of the mark distribution? a. 80 b. 90 c. 85 d. 75 e. 95

B

16. The following graph is a normal probability plot for the amount of rainfall in acre-feet obtained from 26 randomly selected clouds that were seeded with silver oxide: a. The data appear to show exponential growth; that is, the amount of rainfall increases exponentially as the amount of silver oxide increases. b. The pattern suggests that the measurement is not normally distributed. c. A least squares regression line should be fitted to the rainfall variable. d. It can be expected that the histogram of rainfall amount will look like the normal curve. e. The shape of the curve suggests that rainfall is caused by seeding the clouds with silver oxide.

E

17. The marks on a statistics test are normally distributed with a mean of 62 and a variance of 225. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what mark is required to get a B or higher? a. 68.7 b. 71.5 c. 73.2 d. 74.6 e. 69.9

B

18. The following is an ogive on the number of ounces of alcohol (one ounce is about 30 mL) consumed per week in a sample of 150 students. A study wished to classify the students as "light", "moderate", "heavy" and "problem" drinkers by the amount consumed per week. About what percentage of students are moderate drinkers, i.e., consume between 4 and 8 ounces per week? a. 20% b. 40% c. 50% d. 60% e. 80%

E

20. The grade point averages of students at the University of Georgia are approximately normally distributed with mean equal to 2.4 and standard deviation equal to 0.8. What fraction of the students will possess a grade point average in excess of 3.0 ? a. .7500 b. .6000 c. .2734 d. .2500 e. .2266

D

21. The diameters of steel disks produced in a plant are normally distributed with a mean of 2.5 cm and standard deviation of .02 cm. The probability that a disk picked at random has a diameter greater than 2.54 cm is about: a. .5080 b. .2000 c. .1587 d. .0228 e. .4920

C

22. In some courses (but certainly not in an intro stats course!), students are graded on a "normal curve". For example, students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B; between 1.5 and 2.0 standard deviations above the mean receive a B+, etc. The class average in an exam was 60 with a standard deviation of 10. The bounds for a B grade and the percentage of students who will receive a B grade if the marks are actually normal distributed are: a. (65, 75), 24.17% b. (70, 75), 18.38% c. (70, 75), 9.19% d. (65, 75), 12.08% e. (70, 75), 6.68%

B

23. Refer to the previous question. Another instructor decides that the lower "B" cutoff should be the 70th percentile. The lower-cutoff for a B grade is: a. 70 b. 65 c. 60 d. 75 e. 80

E

24. Suppose the test scores of 600 students are normally distributed with a mean of 76 and standard deviation of 8. The number of students scoring between 70 and 82 is: a. 272 b. 164 c. 260 d. 136 e. 328

A

25. Bolts that are used in the construction of an electric transformer are supposed to be 0.060 inches in diameter, and any bolt with diameter less than 0.058 inches or greater than 0.062 inches must be scrapped. The machine that makes these bolts is set to produce bolts of 0.060 inches in diameter, but it actually produces bolts with diameters following a normal distribution with inches and inches. The proportion of bolts that must be scrapped is equal to: a. 0.0456 b. 0.0228 c. 0.9772 d. 0.3333 e. 0.1667

D

26. The cost of treatment per patient for a certain medical problem was modeled by one insurance company as a normal random variable with mean $775 and standard deviation $150. What is the probability that the treatment cost of a patient is less than $1,000, based on this model? a. .5000 b. .6826 c. .8531 d. .9332 e. Cannot be computed without knowledge of additional parameters

B

27. The time that a skier takes on a downhill course has a normal distribution with a mean of 12.3 minutes and standard deviation of 0.4 minutes. The probability that on a random run the skier takes between 12.1 and 12.5 minutes is: a. 0.1915 b. 0.3830 c. 0.3085 d. 0.6170 e. 0.6826

E

28. It is known that the resistance of carbon resistors is normally distributed with ohms and ohms. What proportion of the resistors have resistances that differ from the mean resistance by more than 120 ohms? a. 0.9544 b. 0.3413 c. 0.1587 d. 0.6826 e. 0.3174

B

29. The time required to assemble an electronic component is normally distributed with a mean of 12 minutes and a standard deviation of 1.5 min. Find the probability that a particular assembly takes more than 14.25 minutes. a. .9332 b. .0668 c. .3413 d. .4332 e. .1587

C

3. The yield of a variety of wheat was measured on a series of small plots. The 2nd and 98th percentiles were found to be 29 bushels/acre and 41 bushels/acre respectively. The standard deviation (bushels/acre) is approximately: a. 12 b. 6 c. 3 d. 4 e. 2

B

4. If a store runs out of advertised material during a sale, customers become upset, and the firm loses not only the sale, but also goodwill. From past experience, a record store finds that the mean number of albums sold in a sale is 845, the variance is 225, and that a histogram of the demand appears mound shaped. The manager is willing to accept a 2.5% chance that an album will be sold out. About how many albums should the manager order for an upcoming sale? a. 1295 b. 875 c. 1070 d. 935 e. 84

A

40. The measurement of the width of the index finger of a human right hand is a normally distributed variable with a mean of 6 cm. and a standard deviation of 0.5 cm. What is the probability that the finger width of a randomly selected person will be between 5 cm. and 7.5 cm.? a. .9759 b. .0241 c. .9500 d. 1.000 e. not within ± 0.001 of these

D

41. Lice are a pesky problem for school aged children and is unrelated to cleanliness. The lifetimes of lice that have fallen off the scalp onto bedding is approximately normally distributed with a mean of 2.2 days and a standard deviation of 0.4 days. We would expect that approximately 90% of the lice would die within: a. about 2.6 days b. about 3.9 days c. about 2.5 days d. about 2.7 days e. about 3.0 days

A

42. The length of time it takes to find a parking spot, during the summer terms on a campus, follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. The probability that a student, attending classes during the summer terms, will find a parking spot in less than 3 minutes is a. .3085 b. .6915 c. .8085 d. .1915

C

43. Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete the quiz is uniformly distributed over the interval [0, 15]. Suppose a student from the class is selected at random, what is the probability that the student will take more than 10 minutes to complete the quiz? a. 1/30 b. 1 c. 1/3 d. 1/2

A

44. Which of the following does not apply to the normal distribution? a. The normal curve is symmetrical about its standard deviation b. The normal curve is unimodal c. The mean, the median and the mode are all equal to each other d. The total area under the normal curve is 1

B

45. Below, the cumulative frequency plot shows height (in inches) of college basketball players. What is the interquartile range a. 3 inches b. 6 inches c. 25 inches d. 50 inches e. None of the above

D

46. Suppose that family incomes in a town are normally distributed with a mean of $1,200 and a standard deviation of $600 per month. The probability that a given family has an income over $2,000 per month is a. 0.9082 b. 0.5918 c. 0.4082 d. 0.0912

B

47. Consider the following ogive of the scores of students in an introductory statistics course: A grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students that obtained a grade of C or C+ is: a. 15% b. 20% c. 25% d. 30% e. 50%

C

5. The output from a sewage treatment plant is constantly monitored to assess treatment efficacy. Suppose that the mean coliform content is 20 bacteria/ml with a standard deviation of 4 bacteria/ml and the distribution is mound shaped. An automatic measuring device is being used to monitor the bacterial levels. An alarm should ring whenever the bacterial level exceeds the 97.5th percentile. The upper bound should be: a. 20 per ml b. 24 per ml c. 28 per ml d. 32 per ml e. 16 per ml

D

6. A researcher is studying the hatching times of Yellow Bellied Sapsuckers. She has a study group of 40 eggs. A similar study has shown that the eggs' hatching times should have a mean of 42 days and a variance of 9 days. Her thesis advisor has suggested that the distribution of hatching times will have the same shape as that of the Purple Throated Tree-tappers, which is "mound shaped". If the researcher is willing to assume that her advisor is correct, how may eggs will have hatching times between 36 and 48 days? a. Approximately 55% or around 22 eggs. b. Approximately 68% or around 27 eggs. c. Approximately 75% or around 30 eggs. d. Approximately 95% or around 38 eggs. e. Almost all of the eggs.

B

8. The average time between infection with the AIDS virus and developing AIDS has been estimated to be 8 years with a standard deviation of about 2 years and bell shaped. Approximately what fraction of people develop AIDS within 4 years of infection? a. 5% b. 2.5% c. 32% d. 16% e. 1%

D

9. A manufacturer of steel pipes produces pipes that are supposed to measure 4 inches in diameter. The actual measurements of the pipes are variable but follow a normal distribution, with a mean of 4 inches and a standard deviation of .04 inches. If the distribution of this variable (actual measurements of the pipes) is bell-shaped, approximately ____ % of the pipes will be between 3.92 inches and 4.08 inches. a. 68 b. 75 c. 89 d. 95 e. 99.7