AP STATS FINAL
A campus has 55% male and 45% female students. Suppose 30% of the male students pick basketball as their favorite sport compared to 20% of the females. If a randomly chosen student picks basketball as the student's favorite sport, what is the probability the student is male?
(.55)(.30)/(.55)(.30)+(.45)(.20)
A coin is weighted so that heads is twice as likely to occur as tails. The coin is flipped repeatedly until a tails occurs. Let X be the number of flips made. What is the most probable value for X?
1
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?
2.415
The five-number summary for a data set is given by min = 5, Q1 = 18, median = 20, Q3 = = 40, max = 75. If you wanted to construct a boxplot for the data set that would show outliers, if any existed, what would be the maximum possible length of the right-side "whisker"?
33
In tossing a fair coin, which of the following sequences is more likely to appear?
HHHHH
A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed: - If there is no response or if an answering machine is reached, another number is automatically called. • If a person answers, a survey worker verifies that the person is least 18 years of age. • If the person is not at least 18 years of age, no response recorded, and another number is called. • If the person is at least 18 years of age, that person is surveyed.
Registered voters with children under the age of 18 years may be underrepresented in the sample
The researcher thinks she can improve her chances by running five identical hypotheses tests, each using a different group of diabetic volunteers, hoping that at least one of the tests will show that her new oral diabetes medication helps control blood sugar level better than insulin injection. What is the probability of committing at least one Type I Error? Note: the probability of committing a Type I Error is 5%.
1-(.95)^5
A recent study noted prices and battery lives of 10 top-selling tablet computers. The data follow: What is the model's predicted battery life for the tablet computer costing $480?
10 hr
When people order books from a popular online source, they are shipped in boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
3.02
Suppose we have a random variable X where the probability associated with the value (10k)(.38)^k(.62)^10-k for k= -, ..., 10 What is the mean of X?
3.8
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?
3/15
The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds in a standard deviation of 50 pounds the weight of adult female grizzly bears approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds approximately what would be the weight of a female grizzly bear with the same standardized Z score as a male grizzly bear with a weight of 530 pounds?
324 pounds
Records from a dairy farm yielded the following information on the number of male and female calves born at various times of the day. What is the probability that a randomly selected calf was born in the night or was a female?
369/513
Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?
4(1/6)^1(5/6)^3
The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5% of bags that have too few briquets. What is the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free?
418
Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6%, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0%
6th percentile
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?
700 mg to 740 mg
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?
78/212
A school is having a contest in which students guess the number of candies in a jar. The student whose guess is the closest to the correct number of candies in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back stemplot below. Which of the following statements is true about the distribution of guesses?
The distribution of guesses for males and females are both skewed to the left
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 Max = 24 Lower quartile = 15 Upper quartile = 18 Median = 16 n = 10
The largest observation is 24 and it is an outlier. No other observation sin the data set could be outliers.
The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine has 20 towels in it, the manager flips a coin to determine which detergent will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. What is the design of this experiment?
A completely randomized block design
An agronomist wants to test three different types of fertilizer (A, B, and C) on the yield of a new variety of wheat. The yield will be measured in bushels per acre. Six 1-acre plots of land were randomly assigned to each of the three fertilizers. The treatment, experimental unit, and response variable are, respectively,
A specific fertilizer, a plot of land, wheat yield
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 fourth year students to complete a questionnaire. Which of the following best describes the principal's sampling plan?
A stratified random sample
On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?
All people who voted in the poll
A 100-question multiple-choice history exam is graded as number correct minus ! " number incorrect, so scores can take values from -25 to +100. Suppose the standard deviation for one class's results is reported to be -3.14. What is the proper conclusion?
An error was made in calculating standard deviation
A simple random sample is defined by
the method of selection
A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket: $500 = 0.01 $100 = 0.05 $25 = .20 $0 = .74 Which of the following are the mean and standard deviation, respectively, of the winnings?
$15, $53.85
A company sells concrete in batches of 5 cubic years. The probability distribution of X, then number of cubic yards sold in a single order for concrete from this company, is shown in the table below. 10 = .15, 15 = 0.25, 20 = .25. 25 = .30, 30 = 0.05
$432.00
Can shoe size be predicted from height? In a random sample of 50 teenagers, the standard deviation in heights was 8.7 cm, while the standard deviation in shoe size was 2.3. The least squares regression equation was: predicted shoe size = -33.6 + .25(height in cm)
(.25)(8.7)/2.3
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?
0.13
The distribution of colors of candies in a bag is as follows. BROWN: .3 RED: .2 YELLOW: .2 GREEN: .2 ORANGE: .1
0.22
In American roulette, there are 18 red pockets, 18 black pockets, and two green pockets (labeled 0 and 00). The ball is equally likely to land in any of the 38 pockets. What is the probability that a player ends up with a positive outcome, that is, makes money, after 50 equal bets on "red" (that is for each of 50 spins of the wheel, the player wins or loses the specified identical dollar bet depending on whether or not the ball lands in a red or nonred pocket, respectively)?
0.303
Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together 1% of the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?
0.8660
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 selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?
0.8704
A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are .01, .03, and .04. If the components fail independently of one another, what is the probability that the device will not fail in one year?
0.922
The probability distribution for the number of heads in four tosses of a coin is given by 0: 0.0625 1: 0.2500 2: 0.3750 3:0.2500 4:0.0625 The probability of getting at least one tail in four tosses of a coin is
0.9375.
Suppose, in a study of mated pairs of soldier beetles, it is found that the measure of the elytron (hardened forewing) length is always 0.5 millimeters longer in the female. What is the correlation between elytron lengths of mated females and males?
1
Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent of U.S. families living in poverty (POV). Data were collected from all 50 states and the District of Columbia, and a regression analysis was conducted. The resulting least-squares regression line is given by 2534 = 59.2 − 0.620(89:;) with <% = 0.802 . Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?
For each 1% increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.
An AP Statistics student in a large high school plans to survey his fellow students with regard to their preference between using a laptop or using a tablet. Which of the following survey methods is unbiased?
None of the above sampling methods are unbiased
The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value of 19.0 in the output?
On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish
A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. What would be a proper way to use a table of random digits to do this?
One digit from te random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers
In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll?
Response bias
A particular car is tested for stopping distance in feet on wet pavement at 30 mph using tires with one tread design and then tires with another tread design. For each set of tires, the test is repeated 30 times, and the following parallel boxplots give a comparison of the resulting five-number summaries. Which of the following is a reasonable conclusion?
The mean of the distribution 1 is greater than the mean of distribution 2
n a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was "horrible" and 9 was "excellent". For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot below was constructed. The horizontal axis represents the student rating, and the vertical axis represents the parent rating. Thus, an individual data point would represent the rating of a single movie. Which of the following statements is justified by the scatterplot?
The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give higher scores.
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?
To decrease the variability in estimates of the mean commuting time
Zucchini weights are approximately normally distributed with mean 0.8 pound and standard deviation 0.25 pound. Which of the following shaded regions best represents the probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds?
WHITE SPACE ON LEFT
The following are the graphs of three normal curves and three cumulative distribution graphs: Which normal curve corresponds to which cumulative curve?
X and 1, Y and 2, Z and 3 (REMEMBER, X1, Y2, Z3)
A large company is interested in improving the efficiency of its customer service and` decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest 80% of calls will take how long to complete?
less than 10 min
Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6%, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0%
less than the median
A truant officer determines the mean and standard deviation of the number of student absences for all school days during an academic year. Which of the following is the best description of the standard deviation?
Approximately the mean difference between the number of students absent on individual days and the mean number on all days
Should college athletes be required to give their coaches their social media account usernames and passwords? A survey of student-athletes is to be taken. The statistician believes that Division I, II, and III players may differ in their views, so she selects a random sample of athletes from each division to survey. This is a
stratified sample
A coin is weighted so that the probability of heads is 0.6. The coin is tossed 20 times, and the number of heads is noted. This procedure is repeated a total of 200 times, and the number of heads is recorded each time. What kind of distribution has been simulated?
the binomial distribution with n = 20 and p = .6
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 tandard 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?
Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne
A cattle vegetarian is considering two experimental designs to compare two sources of bovine growth hormone, or BVH, to spur increased milk production in Guernsey cattle. Design 1 involves flipping a coin as each cow enters the stockage, and if heads, giving it BVH form bovine cadavers, and if tails, giving it BVH from engineered E. coli. Design 2 involves flipping a coin as each cow enters the stockade, and if heads, giving it BVH from bovine cadavers for a specified period of time and then switching to BVH from engineered E. coli for the same period of time, and if tails, the order is reversed. With both designs, daily milk production is noted. Which of the following is accurate?
Design 1 is a completely randomized design, while Design 2 is a block design
A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded to whether or not they own a car and the location of the home where they live the results are shown in the table below. Which of the following statements about a randomly chosen person from these 200 employees is true?
If the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.
Which of the following is a true statement about sampling?
If the sample is random, the size of the population usually doesn't matter.
A financial analyst determines the yearly research and development investments for 50 blue chip companies. She notes that the distribution is distinctly not bell-shaped. If the 50-dollar amounts are converted to z-scores, what can be said about the standard deviation of the 50 z-scores.
It equals 1
Heights, in inches, for the 200 graduating seniors from Washington Hihg School are summarized in the frequency table below. Which of the following statements about the median height is true?
It is greater than or equal to 60 inches but less than 66 inches.
The kelvin is a unit of measurement for temperature; 0 K is absolute zero, the temperature at which all thermal motion ceases. Conversion from Fahrenheit to Kelvin is given by ! = # $ ($ − 32) + 273. The average daily temperature in Monrovia, Liberia is 78.35℉ with a standard deviation of 6.3℉. If a scientist converts Monrovia daily temperatures to the Kelvin scale, what will be the new mean and standard deviation?
Mean 209.75 K; standard deviation 3.5k
It is estimated the 56 percent of Americans have pets. However, favorite pet of choice differs by geographic location and by pet of choice. The results are summarized in the following segmented bar chart. Which of the following is an incorrect conclusion?
More pet owners in the south than in the North answered "other"
A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?
The slope of the least squares regression line increases and the correlation coefficient increases.
A nonprofit organization plans to hold a raffle to raise funds for top rations a total of 1000 raffle tickets will be sold for one dollar each after all the tickets are sold one ticket will be selected a random and its owner will receive $50 the expected value for the next game for each ticket is -$.95 what is the meaning of the expected value in this context.
The ticket owners lose an average of $0.95 per raffle ticket.
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?
The z-score of the height measurements
The correlation between the age and height of children under the age of 12 is found to be r = 0.60. Suppose we use the age x of a child to predict the height y of the child. What can we conclude?
Thirty six percent of the variation in height is accounted for by the linear model relating height to age
Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?
at least 50% of the scores in section 3 are higher than all the scores in section 1
You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked to reveal her attitude toward the product. You think there may be large differences in the responses of women who are employed and those who are not. Because of these differences, you should use...
block design, but not a matched pairs design
Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6%, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0%
clearly skewed to the left
