AP STATS CHEAT
A company sells concrete in bathes of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, shown in a table below. x 10 15 20 25 30 Prob .15 .25 .25 .30 .05 The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit, Y, in dollars, for a particular order can be described by Y = 75X -100. What is the standard deviation of Y? (A)$332 (B)$532 (C)$1,343.75 (D)$432
$432
A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
.023
A distribution of scores is approximately normal with a mean of 78 and a standard deviation of 8.6. Which of the following equations can be used to find the score x above which 33 percent of the scores fall?
.44=(x-78)/8.6
All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?
0.00640
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)0.0020 (B)0.0195 (C)0.8889 (D)0.9805 (E)0.9980
0.0195
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?
0.170
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 one 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) 0.100 (B) 0.200 (C) 0.250 (D) 0.325 (E) 0.400
0.400
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? (A) 0.0256 (B) 0.1296 (C) 0.3456 (D) 0.8704 (E) 0.9744
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 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year? (A)Less than 0.01 (B)0.078 (C)0.080 (D)0.922 (E)Greater than 0.99
0.922
a sleep time of 15.9 hours per day for a newborn baby is the 10th percentile of the distribution of sleep times for all newborn babies. assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day for newborns?
16.5
A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y.
17.5
A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?
2
A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags? (A)13.5 (B)14.5 (C)15.0 (D)27.0 (E)29.0
29.0
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
700 mg to 740 mg
Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What score did this student receive on the test?
779.42
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 study was conducted to evaluate the impact of taking a nutritional 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 randomized block design
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist?
An experiment with a completely randomized design
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?
Because the participants were self-selected, a person's desire to be cured could be a confounding variable.
A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this? (A)Block on dog breed and randomly assign puppies to existing and new formula groups within each breed. (B)Block on geographic location and randomly assign puppies to existing and new formula groups within each geographic area. (C)Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by breed to either the existing or the new formula. (D)Stratify on geographic location of the puppies and randomly sample puppies within each geographic area. Then assign puppies by geographic area to either the existing or the new formula (E)Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by gender to either the existing or the new formula.
Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
A field researcher who studies lions conjectures that the more time a cub spends playing, the sooner a cub begin to hunt
For female Cubs only
A local television news station includes a viewer survey question about a current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The results of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the results of such surveys could be biased? I. Viewers with strong opinions about the current issue are more likely to respond than are viewers without strong opinions. II. The opinions of viewers of one television station are not necessarily representative of the population of a region. III. Viewers with access to social media are not necessarily representative of the population of a region.
I, II and III
A well-designed experiment should have which of the following characteristics? I. Subjects assigned randomly to treatments II. A control group or at least two treatment groups III. Replication
I, II, and III
A compact disc (CD) manufacturer wanted to determine which of the two different cover dish s for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CD's with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion? A. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment B. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because there was no control group for comparison C. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because the 70 stores were not randomly chosen D. It is reasonable to conclude that the difference in sales was caused by the different cover deigns because the cover designs were randomly assigned to stores E. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large
It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores
A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?
Many of the people selected to participate in the survey who do not respond might have different opinions from those who do respond.
A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of the two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?
Only people aged nineteen to thirty living in the state of Colorado.
According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent 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?
Not enough information is given to determine the probability.
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?
Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.
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 verifies that the person is at least 18 years of age. - If the person is not at least 18 years of age, no response is recorded, and another number is called. - If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used?
Registered voters with children under the age of 18 years may be underrepresented in the sample.
A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table.Based on the data in the table, which of the following is the appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification.
Segmented bar chart
A school is having a contest in which students guess the number of candies in a jar. The student whose guess is 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 distributions of guesses?
The distributions of guesses for male and female students are both skewed to the left.
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?
The height increases, on average, by 0.29 meter each year
A scatter plot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One point is labeled A
The slope of the lsrl increases and the correlation coefficient increases
A new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. The times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute-425 degree combination. That combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. The quality of the finished product is evaluated for each roast. Which of the following is true?
The two cuts that are being roasted for each time-temperature combination are an example of replication
A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the numbers of students by employment status (job, no job) and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?
There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.
An agricultural scientist wanted to compare the effect of new fertilizer to that of three older fertilizers—X, Y, and Z—on the growth of vegetables typically grown in small gardens. Two hundred green bean seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each. Seedlings in one group were given the new fertilizer, and the three remaining groups of seedlings were given fertilizers X, Y, or Z, respectively. At the end of four weeks, all seedlings were dried and weighed. The scientist found that the mean weight of the seedlings in the group given the new fertilizer was significantly greater than the mean weights of seedlings in the other three groups. The scientist concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is the scientist's conclusion not appropriate?
lacked a control group that did not use any fertilizer
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?
participants within each block should be as similar as possible with respect to how easily they get sunburned
a newspaper editor wants to investigate whether residents of the study support a proposal to build a new high school football stadium. the editor hires a send a survey polling firm to conduct a survey and requests that a sample of 500 residents be selected using stratified sampling design based on the voting within the city. which of the following methods will achieve the desired sampling design? a. send a survey to all city residents and use the first 500 returned surveys for a sample b. select a random sample from each voting district based on the the proportion of city residents in that district so that a total of 500 is obtained c. select one voting district at random and then select a random sample of 500 from the selected voting district d. alphabetize the list of all city residents and then select the first 500 residents on the list classifying those selected by voting district e. select the first 500 citizens who attend the next high school football game
select a random sample from each voting district based on the the proportion of city residents in that district so that a total of 500 is obtained
A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has a mean 14.1 pounds and a standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has a mean 6.7 pounds and a standard deviation of 0.5 pounds. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W? A) 1.3+0.5 B) sqrt(1.3^2+0.5^2) C) sqrt(10(1.3)^2+15(0.5)^2) D) sqrt(10^2(1.3)^2+15^2(0.5)^2) E) sqrt((1.3)^2/10 + (0.5)^2/15
sqrt(10(1.3)^2+15(0.5)^2)
A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is a 1 or 2. How many dice should the player choose to roll to maximize the chance of winning? (A)two (B)four (C)six (D)eight (E)ten
two
