AP Stat

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. Which of the following values is closest to the standard deviation of the 100 times? (A) 2.5 seconds (B) 10 seconds (C) 20 seconds (D) 50 seconds (E) 90 seconds

B

If a probability distribution is symmetric, which of the following statements must be true? (A) The distribution is normal. (B) The distribution is uniform. (C) The distribution is bimodal. (D) The mean of the distribution is equal to the median of the distribution. (E) The interquartile range of the distribution is equal to the standard deviation of the distribution

D

A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal selected at random samples of 50 first-year students, 50 second-year students, 50 third-year students, and 50 fourthyear students to complete a questionnaire. Which of the following best describes the principal's sampling plan? (A) A stratified random sample (B) A simple random sample (C) A cluster sample (D) A convenience sample (E) A systematic sample

A

A researcher wishes to calculate the average height of patients suffering from a particular disease. From patient records, the mean was computed as 156 cm, and standard deviation as 5 cm. Further investigation reveals that the scale was misaligned, and that all readings are 2 cm too large, for example, a patient whose height is really 180 cm was measured as 182 cm. Furthermore, the researcher would like to work with statistics based on meters. The correct mean and standard deviation are: (a) 1.56m, 0.05m (b) 1.54m, 0.05m (c) 1.56m, 0.03m, (d) 1.58m, 0.05m, (e) 1.58m, 0.07m

B

Mr. Yates picked up a dozen items in the grocery store with a mean cost of $3.25. Then he added an apple pie for $6.50. The new mean for all 13 items is (a) $3.00 (b) $3.50 (c) $3.75 (d) $4.88 (e) None of the above

B

The distribution of the heights of students in a large class is roughly normal. 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

B

The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Half of all young men are shorter than (a) 65.5 inches (b) 68 inches (c) 70.5 inches (d) can't tell, because the median height is not given (e) none of the above

B

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6? (A) 2/36 (B) 3/36 (C) 3/15 (D) 2/9 (E) 4/6

C

A police officer is using a radar device to check motorists' speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's estimate is correct, what is the probability that among 4 randomly selectedmotorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit? (A) 0.0256 (B) 0.1296 (C) 0.3456 (D) 0.8704 (E) 0.9744

D

A randomized block design will be used in an experiment to compare two lotions that protect people from getting sunburned. Which of the following should guide the formation of the blocks? (A) Participants in the same block should receive the same lotion. (B) Participants should be randomly assigned to the blocks. (C) Participants should be kept blind as to which block they are in. (D) Participants within each block should be as similar as possible with respect to how easily they get sunburned. (E) Participants within each block should be as different as possible with respect to how easily they get sunburned.

D

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

D

If the median of a set of data is equal to the mean, then (a) The data are Normally distributed. (b) The data are approximately Normally distributed. (c) The distribution is skewed. (d) The distribution is symmetric. (e) One can't say anything about the shape of the distribution without any certainty.

E

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah's height, and how does her height compare to Jayne's height? (A) Aliyaah's height is at the 17th percentile of the distribution, and she is shorter than Jayne. (B) Aliyaah's height is at the 67th percentile of the distribution, and she is shorter than Jayne. (C) Aliyaah's height is at the 67th percentile of the distribution, and she is taller than Jayne. (D) Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne. (E) Aliyaah's height is at the 83rd percentile of the distribution, and she is taller than Jayne.

D

Two college roommates have each committed to donating to charity each week for the next year. The roommates' weekly incomes are independent of each other. Suppose the amount donated in a week by one roommate is approximately normal with mean $30 and standard deviation $10, and the amount donated in a week by the other roommate is approximately normal with mean $60 and standard deviation $20. Which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $120? (A) 0; the combined donation never exceeds $120 in a week (B) 1 week (C) 3 weeks (D) 5 weeks (E) 8 weeks

D

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg). If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights? (A) 740 mg to 780 mg (B) 700 mg to 740 mg (C) 680 mg to 720 mg (D) 660 mg to 700 mg (E) 620 mg to 660 mg

B

The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights outside the range (a) 65.5 inches to 70.5 inches (b) 63 inches to 73 inches (c) 60.5 inches to 75.5 inches (d) 58 inches to 78 inches (e) none of the above

B

Which of the following is likely to have a mean that is smaller than the median? (a) The salaries of all National Football League players. (b) The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores but a few do very poorly. (c) The prices of homes in a large city. (d) The scores of students (out of 100 points) on a very difficult exam in which most get poor scores but a few do very well. (e) Amounts awarded by civil court juries.

B

"Normal" body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5° C with a standard deviation of 0.3° C. When converted to °F, the mean and standard deviation are (°F = °C(1.8) + 32). (a) 97.7, 32 (b) 97.7, 0.30 (c) 97.7, 0.54 (d) 97.7, 0.97 (e) 97.7, 1.80

C

A certain motel is roughly 20 miles from the entrance to Yosemite National Park. The motel manager wants to get a better estimate of the distance and asks five people to each measure the distance, to the nearest tenth of a mile, using the odometer in his or her car. The manager will use the median of the five measurements as the estimate of the distance. Which of the following statements is NOT a statistical justification for the manager's plan? (A) Odometer reading should be considered a variable when used to measure this distance. (B) The median of the five measurements is more likely to be close to the actual distance than is a single measurement. (C) The actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance. (D) If one or two odometers give inaccurate readings, the estimate still should be fairly close to the actual distance. (E) The manager can get some indication of how far off the estimate might be.

C

If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men? (Assume the heights of American Men are Normally Distributed). A.) 1" B.) 2" C.) 4" D.) 6" E.) 12"

C

A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph? (A) The mean is greater than the median. (B) The median is the average of the first quartile and the third quartile. (C) There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile. (D) There are more selling prices that are less than the mean than selling prices that are greater than the mean. (E) The value of maximum minus third quartile is less than the value of first quartile minus minimum.

E

Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure? (A) The mean of the height measurements (B) The median of the height measurements (C) The standard deviation of the height measurements (D) The maximum of the height measurements (E) The z-scores of the height measurements

E

Many professional schools require applicants to take a standardized test. Suppose that 1000 students take the test, and you find that your mark of 63/100 is the 73rd percentile. This means that a) at least 73% of the people scored a 63 or better b) at least 270 people scored 73 or better c) at least 730 people scored 73 or better d) at least 27% of the people scored 73 or worse e) at least 270 people scored 63 or better

E

The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min = 12 Lower quartile = 15 Median = 16 Max = 24 Upper quartile = 18 n = 10 Which of the following statements is true? (A) The smallest observation is 12 and it is an outlier. No other observations in the data set could be outliers. (B) The largest observation is 24 and it is an outlier. No other observations in the data set could be outliers. (C) Both 12 and 24 are outliers. It is possible that there are also other outliers. (D) 12 is an outlier and it is possible that there are other outliers at the low end of the data set. There are no outliers at the high end of the data set. (E) 24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

E

Which of the following is NOT CORRECT about a standard normal distribution? (a) P(0 ? Z ? 1.50) = .4332 (b) P(Z ? ?1.0) = .1587 (c) P(Z ? 2.0) = .0228 (d) P(Z ? 1.5) = .9332 (e) P(Z ? ?2.5) = .4938

E

An experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flash cards or by practicing on a computer. Children who volunteer for the experiment will be randomly assigned to one of the two treatments. Because the children's gender may affect the outcome, there will be blocking by gender. After practice, the children will be given a test on their multiplication facts. Why will it be impossible to conduct a double-blind experiment? (A) The experimenter will know whether the child is a boy or a girl and whether he or she used flash cards or the computer. (B) The child will know whether he or she is a boy or a girl. (C) The child will know whether he or she used flash cards or the computer. (D) The person who grades the tests will know whether the child was a boy or a girl. (E) The person who grades the tests will know whether the child used flash cards or the computer.

C

There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the (a) mean age will stay the same but the variance will increase. (b) mean age will stay the same but the variance will decrease. (c) mean age and variance will stay the same. (d) mean age and variance will increase. (e) mean age and variance will decrease.

B

A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? (a) Your friend must not have followed the diet correctly, since she did not lose weight. (b) Since your friend did not lose weight, the report must not be correct. (c) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results. (d) In order for the study to be correct, we must now add your friend's results to those of the study and recompute the new average. (e) Your friend is an outlier.

C

A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as "30" actually had a value of "35." If we make this correction to the data, then a) the mean remains the same, but the median is increased. b) the mean and median remain the same. c) the median remains the same, but the mean is increased. d) the mean and median are both increased. e) we do not know how the mean and median are affected without further calculations, but the variance is increased.

C

A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is, a fish that really weighed 26 g was reported to weight 24 g. What are the mean and standard deviation after correcting for the error in the scale? a) 28 g, 2 g b) 30 g, 4 g c) 32 g, 2 g d) 32 g, 4 g e) 28 g, 4 g

C

Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum? (A) 1.708 (B) 1.848 (C) 2.415 (D) 3.416 (E) 5.835

C

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will contain between 16.0 and 16.1 ounces is about? (a) 10 (b) 16 (c) 34 (d) 68 (e) none of the above

C

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, that is consume between 4 and 8 ounces per week? (a) 60% (b) 20% (c) 40% (d) 80% (e) 50%

C

When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (ppm). 5, 7, 12, bdl, 10, 8, bdl, 20, 6 Which of the following is correct? (a) The mean lead level in the water is about 10 ppm. (b) The mean lead level in the water is about 8 ppm. (c) The median lead level in the water is 7 ppm. (d) The median lead level in the water is 8 ppm. (e) Neither the mean nor the median can be computed because some values are unknown.

C

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course? (A) 0.45 (B) 0.32 (C) 0.20 (D) 0.13 (E) 0.05

D

Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends' scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in a single game? (A) 0.16 (B) 0.28 (C) 0.31 (D) 0.33 (E) 0.37

D

Which of the following statements is NOT true? (a) In a symmetric distribution, the mean and the median are equal. (b) The first quartile is equivalent to the twenty-fifth percentile. (c) In a symmetric distribution, the median is halfway between the first and third quartiles. (d) The median is always greater than the mean. (e) The range is the difference between the largest and the smallest observation in the data set.

D

A regional transportation authority is interested in estimating the mean number of minutes working adults in the region spend commuting to work on a typical day. A random sample of working adults will be selected from each of three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend commuting to work on a typical day. Why is stratification used in this situation? (A) To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas (B) To remove bias when estimating the mean commuting time (C) To reduce bias when estimating the mean commuting time (D) To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and rural areas (E) To decrease the variability in estimates of the mean commuting time

E

Consumers' Union measured the gas mileage in miles per gallon of 38 1978-1979 model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers Union. Based on the pie chart, we may conclude that: (a) Japanese cars get significantly lower gas mileage than cars of other countries. This is because their slice of the pie is at the bottom of the chart. (b) U.S cars get significantly higher gas mileage than cars from other countries. (c) Swedish cars get gas mileages that are between those of Japanese and U.S. cars. (d) Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested. (e) More than half of the cars in the study were from the United States.

E

The following is a histogram showing the actual frequency of the closing prices on the New York exchange of a particular stock. Based on the frequency histogram for New York Stock exchange, the class that contains the 80th percentile is: (a) 20-30 (b) 10-20 (c) 40-50 (d) 50-60 (e) 30-40

E

The weights of the male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? (a) About 50% of the male students have weights between 150 and 185 pounds. (b) About 25% of female students have weights more than 130 pounds. (c) The median weight of male students is about 162 pounds. (d) The mean weight of female students is about 120 pounds because of symmetry. (e) The male students have less variability than the female students.

E