AP Stat Cumulative 1-6

Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than a. $360 b. $144 c. $255 d. $216 e. $300

$255

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the expected cost per customer for the performance? a. $2.75 b. $24.50 c. $29.40 d. $2.45 e. $36.00

$29.4

The histogram shown summarizes the responses of 100 people when asked, "What was the price of the last meal you purchased?" Based on the histogram, which of the following could be the interquartile range of the prices? a. $5 b. $3 c. $21 d. $10 e. $40

$5

A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water? a. 0.8889 b. 0.0195 c. 0.0020 d. 0.9805 e. 0.9980

0.0195

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly's commute time tomorrow will be greater than 25 minutes? a. 0.0950 b. 0.0056 c. 0.0894 d. 0.9006 e. 0.8055

0.0950

A worn out bottling machine does not properly apply caps to 5% of the bottles it fills. If you randomly select 20 bottles from those produced by this machine, what is the approximate probability that between 2 and 6 (inclusive) caps have been improperly applied? a. 0.26 b. 0.38 c. 0.92 d. 0.74 e. 0.19

0.26

Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a Normal distribution with mean 90 grams and a standard deviation of 1 gram. Using the Empirical Rule, about what percentage of the items will either weigh less than 87 grams or more than 93 grams? a. 94% b. 0.15% c. 0.3% d. 6% e. 99.7%

0.3%

Mrs. Saltarelli selects a random student at Madison High School. Let Event S = the student owns a smartphone, and Event T = the student sends an average of more than 50 texts per day. The Venn diagram below summarizes the probabilities associated with these two events. Which of the following is the probability that a randomly selected student does not send an average of more than 50 texts per day, given that they own a smartphone? a. 0.4 b. 0.2 c. 0.133 d. 0.294 e. 0.333

0.333

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution: What is the probability that a randomly chosen household has at least two personal computers? a. 0.29 b. 0.19 c. 0.20 d. 0.61 e. 0.39

0.39

A contestant's final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects on of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant's final winnings are twice the value of the base amount. If the selected chip is white, the contestant's final winnings are the value of the base amount. What is the probability that a contestant's final winnings are exactly $2,000 ? a. 0.325 b. 0.200 c. 0.100 d. 0.400 e. 0.250

0.400

If you draw an M&M candy at random from a bag, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color. What is the probability that you do not draw a red candy? a. This is impossible to determine from the information given. b. 0.3 c. 0.2 d. 0.7 e. 0.8

0.8

Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale? a. -1 b. -0.75 c. 0 d. 1 e. 0.75

1

Jackson Maloney makes 80% of his free throws. Suppose this probability is the same for each free throw he attempts, and free throw attempts are independent. The expected number of free throws required until he makes his first free throw of the season is a. 0.31. b. 1.25. c. 0.80. d. 2. e. 0.13

1.25

Like most animals, small marine crustaceans are not able to digest all the food they eat. Moreover, the percentage of food eaten that is assimilated (that is, digested) decreases as the amount of food eaten increases. A scatterplot of ln(assimilation) versus ln(food intake) is strongly linear, suggesting that a linear regression of these transformed variables may be more appropriate. Below is a computer regression analysis of the transformed data (note that natural logarithms are used). When food intake is 250 mg/day, what is the predicted assimilation rate from this model? a. 54.4% b. 27.4% c. 15.4% d. 2.7% e. 34.3%

15.4%

The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? a. 15 b. 50 c. 25 d. 35 e. 20

35

The 35th percentile of a population is the number x such that... a. 65% of the population scores are below x. b. 35% of the population scores are less than or equal to x. c. x is 35% of the population mean. d. x is 35% of the population median. e. 35% of the population scores equal x.

35% of the population scores are less than or equal to x

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. 3 week b. 8 week c. 5 week d. 1 week e. 0; the combined donation never exceeds $120 in a week

5 week

To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we score 2 points, if it takes us two tosses we score 1 point, and if we get two tails in a row we score 0. Use the following sequence of random digits to simulate this game as many times as possible. 12975 13258 45144 Based on your simulation, what is the estimated probability of scoring 2 points in this game? a. 7/15 b. 7/11 c. 9/15 d. 5/15 e. 1/4

7/11

A sample of 942 homeowners are classified, in the two-way frequency table below, by the number of credit cards they have and the number of years they have owned their current homes. Of the homeowners in the sample who have four or more credit cards, what proportion have owned their current homes for at least one year? a. 78/942 b. 78/212 c. 258/942 d. 212/942 e. 78/258

78/212

Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). Which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where F =9/5C + 32? a. 9/5(0.4) + 32 b. (9/5)^2(0.4) c. 9/5(0.4)^2 d. 9/5(0.4) e. (9/5)^2(0.4)^2

9/5(0.4)

A study was conducted to evaluate the impact of taking a supplement on a person's reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study? a. A randomized block design b. A completely randomized design c. A matched-pairs design d. A stratified observational study e. A randomized observational study

A randomized block design

The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city's effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department? a. A census b. An experiment with a randomized block design c. A sample survey d. An experiment with a completely randomized design e. An experiment with a matched-pairs design

A sample survey

A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medicine. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of two groups of equal size. The first group received the current medicine and the second group received the new medicine. When a participant experienced a migraine, he or she was instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, with 1 being no relief to 10 being complete relief. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study? a. An experiment using a matched-pairs design b. An observational study using a stratified sample c. An observational study using a cluster sample d. An experiment using a completely randomized design e. An observational study using a simple random sample

An experiment using a completely randomized design

Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study? a. An observational study was conducted, and the response variable is the depth of the water. b. A census was conducted, and the response variable is the depth of the water. c. An observational study was conducted, and the response variable is the concentration of the chemical. d. An experiment was conducted, and the response variable is the concentration of the chemical. e. An experiment was conducted, and the response variable is the depth of the water.

An observational study was conducted, and the response variable is the concentration of the chemical

A program that was intended to cure a person's fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed they were cured of their fear of spiders. Based on the description of the program, which of the following statements is true? a. Because the participants were self-selected, a person's desire to be cured could be a confounding variable. b. Because the participants were volunteers, the study is a census of all people in the local area who have a fear of spiders. c. Because over 90% of the participants claimed to be cured, the results can be generalized to the population of all people who have a fear of spiders. d. Because participants held a spider for 15 minutes, the study is an experiment and the results can be generalized to the population of all people who have a fear of spiders. e. Because over 90% of the participants claimed to be cured, the results prove that holding a spider will cure a person's fear of spiders.

Because the participants were self-selected, a person's desire to be cured could be a confounding variable.

At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. If age and preferred method of eating ice cream are independent for those surveyed, which of the following tables shows the distribution of responses?

Categories: Cone, Cup, Total Adults: 50, 20, 70 Children: 100, 40, 140 Total: 150, 60, 210

The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that • the probability of being awarded the first job (event A) is 0.75; • the probability of being awarded the second job (event B) is 0.5; • the probability of being awarded both jobs (event A and B) is 0.375; If the owner's beliefs are correct, which of the following statements must be true concerning even A and event B? a. Event A and event B are not mutually exclusive, and are not independent. b. Event A and event B are mutually exclusive and are not independent. c. Event A and event B are not mutually exclusive and are independent. d. Event A and event B are not mutually exclusive, and independence cannot be determined with the information given. e. Event A and event B are mutually exclusive and are independent.

Event A and Event B are not mutually exclusive and are independent.

The most important advantage of experiments over observational studies is that.. a. experiments can give better evidence of causation. b. an observational study cannot have a response variable. c. experiments are usually easier to carry out. d. observational studies cannot use random samples. e. confounding cannot happen in experiments.

Experiments can give better evidence of causation.

The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts? a. There is a clear, negative association between beer sales and ice cream sales. b. Sales records must be in error. There should be no association between beer and ice cream sales. c. Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer. d. A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. e. It is likely that sales of both beer and ice cream are confounded with a lurking variable, such as seasonal variation in temperature.

It is likely that sales of both beer and ice cream are confounded with a lurking variable, such as seasonal variation in temperature

A graduate student conducted a study of field mice in rural Kansas. The student obtained a sample of 100 field mice and recorded the weight, in grams, of each mouse. After the measurements were taken, it was discovered that the scale was set for ounces. The student adjusted the 100 recorded measurements by multiplying each measurement by 0.035. Which of the following statistics for the weight of the field mice has the same value before and after the adjustment? a. The median b. The mean c. The standard deviation d. The interquartile range e. None of the above

None of the above

According to a report for veterinarians in the United States, 36.5% of households in the United States own dogs and 30.4% of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat? a 0.111 b. Not enough information is given to determine the probability. c. 0.669 d. 0.558 e. 0.331

Not enough information is given to determine the probability

Mr. Fisher has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number of occupants of a randomly selected car on his street. Which of the following could be his model?

Number: 1, 2, 3, 4, >= 5 Probability: 0.5, 0.25, 0.15, 0.06, 0.04

Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true? a. P(E) = 0.4 b. P(D or E) = 0.72 c. P(D or E) = 0.28 d. P(E) = 0.12 e. P(D or E) = 0.9

P(D or E) = 0.72

A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample? a. Randomize the names on the list and then select every tenth student on the randomized list. b. Select all female students on the list. c. Randomly select 50 students on the list who are attending college. d. Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list. e. Randomly select 50 students on the list.

Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.

The Bradley effect is a theory proposed to explain observed discrepancies between voter opinion polls and election outcomes in some elections where a white candidate and a non-white candidate run against each other. The theory proposes that some voters tend to tell pollsters that they are undecided or likely to vote for a non-white candidate, and yet, on election day, vote for the white opponent. This is an example of.. a. response bias. b. undercoverage. c. bias resulting from question wording. d. nonresponse. e. voluntary response bias.

Response bias

The faces of a four-sided fair die are numbered 1 through 4, respectively. For a certain game, the die is tossed and the number that lands facedown is recorded. The table below summarizes the points a player earns for the number that lands facedown. Consider two independent tosses of the die. Let the random variable S represent the sum of the points earned from the two tosses. Which table represents the probability distribution of S?

S: 0, 1, 2, 3, 4 Probability: 0.0625, 0.25, 0.375, 0.25, 0.0625

In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played. The means and standard deviations of the random variables for a particular player are shown in the table below. Assume that X and Y are independent. What are the expected value and the standard deviation of the points per game for the player? a. The expected value is 101.5, and the standard deviation is 63.5. b. The expected value is 4.1, and the standard deviation is 63.5. c. The expected value is 4.1, and the standard deviation is 65.4. d. The expected value is -6.5, and the standard deviation is 63.5. check e. The expected value is -6.5, and the standard deviation is 65.4.

The expected value is -6.5, and the standard deviation is 65.4.

The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? a. The mean is 22 and the standard deviation is 102. b. The mean is 20 and the standard deviation is 102. c. The mean is 22 and the standard deviation is 50. d. The mean is 22 and the standard deviation is 100. e. The mean is 20 and the standard deviation is 50.

The mean is 22 and the standard deviation is 100.

The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Which of the following statements is supported by the table? a. At least 80 people are affiliated with the Green Party or the Libertarians. b. Less than half of the people are affiliated with the Democrats or the Republicans. c. At least 200 people are affiliated with the Democrats. d. The number of people affiliated with the Republicans is 30. e. The number of people affiliated with the Independents is 100.

The number of people affiliated with the Independents is 100.

As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study? a. The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female. b. The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected. c. The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis. d. The population is the 770 students who were selected, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis. e. The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.

The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected

An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48 (age) Which of the following is the best interpretation of the slope of the regression line? a. The predicted height increases, on average, by 0.29 meter each year. b. The predicted height increases, on average, by 0.48 meter each year. c. The predicted height increases, on average, by 1 meter each 0.48 year. check d. The difference between the actual height and the predicted height is, on average, 0.48 meter for each year. e. The predicted height increases, on average, by 0.29 meter each 0.48 year.

The predicted height increases, on average, by 0.48 meter each year

The probability of any outcome of a random phenomenon is a. none of the other answer choices are correct. b. the proportion of times the outcome occurs in a very long series of trials. c. the precise degree of randomness present in the phenomenon. d. any number as long as it is greater than 0 and less than 1. e. either 0 or 1, depending on whether or not the phenomenon can actually occur or not.

The proportion of times the outcome occurs in a very long series of trials.

A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds' total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the road runner? a. Overestimate, because the residual is negative. b. Underestimate, because the residual is negative. c. Neither, because the residual is 0. d. Overestimate, because the residual is positive. e. Underestimate, because the residual is positive.

Underestimate, because the residual is positive

An experiment compares the taste of a new spaghetti sauce with the taste of a commercially successful sauce readily available in grocery stores. Each of a number of tasters tastes both sauces (in random order) and says which tastes better. This experiment is called a... a. matched pairs design. b. simple random sample. c. completely randomized design. d. stratified random sample. e. double-blind design.

a. matched pairs design

A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. • 20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major. • 30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major. • 50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major? a. 0.960 b. 0.400 c. 0.170 d. 0.125 e. 0.045

c. 0.170

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is: a. μ=1.6;σ=1.414 b. μ=2;σ=1.6 c. μ=2;σ=1.265 d. μ=1.6;σ=1.265 e. μ=2;σ=1.414

u = 2, o = 1.265

Just before the presidential election of 1936, the magazine Literary Digest predicted—incorrectly, as it turned out—that Alf Landon would defeat Franklin Delano Roosevelt. Landon lost in a landslide. It turned out that the magazine had only polled its own subscribers, plus others from a list of automobile owners and a list of people who had telephone service. All three groups had higher than typical incomes during the Great Depression. This is an example of.. a. nonresponse. b. undercoverage. c. response bias. d. bias resulting from question wording. e. voluntary response bias.

undercoverage

Ms. Wahle selects two cards from a deck of 52 cards and observes the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space for the possible outcomes? a. {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red." b. {0, 1, 2}. c. {red, black} d. All of the other answer choices are correct. e. {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

{(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."