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Statistics Review

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A medical device company knows that 11% of patients experience injection-site reactions with the current needle. If 3 people receive injections with this type of needle, what is the probability that the first person has an injection-site reaction, but the next two do not?0.00130.01080.08710.7921

.0871

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. What is the probability that a randomly selected customer will get the classic wash and vacuum their car?0.050.090.120.25

.09

A student surveyed 200 students and determined the number of students who have a dog and have a cat.Let A be the event that the student has a dog and B be the event that the student has a cat. The student finds that P(A) = 0.33, P(B) = 0.50, and P(A and B) = 0.15.What is P(A or B)? Round the answer to two decimal points.

.68

A group of ticket takers at a box office for a new theater noticed that in the first year of the theater's operation, the genre breakdown of the movies was 10% horror, 39% comedy, 28% drama, and 23% action. If a movie from the theater's first year of operation was selected at random, which of the following identifies the probability distribution for the movie's genre?

B ActionComedyDramaHorror0.23 0.39 0.28 0.10

The following two-way table shows the distribution of high school students categorized by their grade level and book-type preference.Suppose a high school student is selected at random. Let event A = junior and event B = fiction. Are events A and B independent?Yes, P(A) = P(A|B).Yes, P(A) = P(B|A).No, P(A) ≠ P(A|B).No, P(A) ≠ P(B|A).

No, P(A) ≠ P(A|B).

Roku rolls 5 fair, 6-sided dice all at once. What is the probability that he rolls all 1s?

(1/6)^5

A biology class conducted an experiment to determine if playing classical music had an effect on the hatching rate of chicken eggs. Here are their results.Let event A = Music and event B = Hatched.Calculate the following:P(A|B) =

.589

A student surveyed 100 students and determined the number of students who take statistics or calculus among seniors and juniors. Here are the results.Let A be the event that the student takes statistics and B be the event that the student is a senior.What is P(Ac or Bc)? Round the answer to two decimal points.

.85

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If three such number cubes are rolled, what is the probability that all three show a number 10 or larger?

(3/12)^3

There are 36 students on the debate team at a school. There are 6 seniors, 12 juniors,10 sophomores, and 8 freshmen on the team. The coach is going to select 4 students at random to participate in the next debate. Calculate the probability that all 4 students are sophomores.0.00360.00600.00840.2778

.0036

Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color. What is the probability that a randomly selected participant dreams in color only?

.05

Suppose that P(A) = 0.42, P(B) = 0.5, and events A and B are independent.What is P(A and B)? Do not round your answer.0.050.210.2750.95

.21

Suppose that P(A) = 0.42, P(B) = 0.5, and events A and B are mutually exclusive.P(A or B) =P(A and B) =

.92 0

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If three such number cubes are rolled, what is the probability that at least 1 of them shows a 2?

0.2297

The daily high temperatures in a vacation resort city are approximately Normal, with a mean temperature of 75 degrees Fahrenheit and a standard deviation of 6 degrees. If a weather forecast predicts the high temperature will be at most 68 degrees, the city provides fewer lifeguards for the city beaches. On what percentage of days will fewer lifeguards be provided?

12.10%

A researcher randomly surveyed 122 college professors to determine what types of courses they teach and their sleeping habits. The two-way table displays the data.Suppose a survey respondent is randomly selected. Let M = professor teaches math and B = professor is an early bird. What is the value of P(B|M)?

16/33

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop by using a random digit table. What is the fewest number of digits that should be used, given that there are 100 plants in total?

A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data.Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)?

20/29

At the Fisher farm, the weights of zucchini squash are Normally distributed, with a mean of 5 ounces and a standard deviation of 0.7 ounces. Which weight represents the 8th percentile?

4.01

Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week's meeting. What is the probability that Greg will not get to pick the café for either of the first two weeks?

4/9

Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here. Payment Method Live CashierSpeed PassTotalVehicle TypeCar3567102Truck184765 Total53114167 What percentage of vehicles are trucks, given that they use Speed Pass?

41.2

Keeping car tires inflated is essential to safe driving. For one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately Normal, with a mean of 35 psi and a standard deviation of 2 psi. What percentage of tires are inflated to a pressure between 33.5 and 36 psi?

46.48

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor a game console. A survey participant is randomly selected. Let M be the event that the participant brought a microwave and let C be the event that the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant brought a microwave or a console, P(M or C)?0.710.860.900.95

????? (It is NOT .95)

A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a continuous quantitative variable that might be included in the brochure?

fuel efficiency (in mpg)

A group of dental researchers are testing the effects of acidic drinks on dental crowns. They have five containers of crowns labeled V, W, X, Y, and Z. They will randomly select one of the containers to be the control for the experiment by drawing one of five well-mixed slips of paper with the same labels from a hat. Which of the following is the probability model for the control container?

A V W X Y Z0.20 0.20 0.20 0.20 0.20

Three siblings, Peyton, Cameron, and Dakota, all ask their parents to borrow the family car for different events around town. Since they cannot all borrow the car at the same time, the parents decide to use randomness to decide who gets the car. They will roll a single, fair, six-sided number cube. Peyton gets the car if a 1 or 2 is rolled. Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a 5 or 6 is rolled. Which of the following is the probability distribution for who gets the car?

B PeytonCameronDakota1/3 1/3 1/3

The following two-way table shows the distribution of pets in a large apartment building.Suppose we select a resident of the apartment building at random.Let event A = Cat and event B = Dog.Calculate and interpret P(A|B).The probability that a randomly selected resident owns a , given that the person also owns a , is equal to approximately

Cat, Dog, .90

Which of the following is not true about cluster sampling?

Cluster sampling has the advantage of reducing sampling variability.

A popular board game has players twist their bodies around so that their hands and feet touch small colored dots. A spinner with equal areas for each body part (left hand, right hand, left foot, or right foot) is used. Which of the following is the correct probability distribution for the body part chosen to be placed?

D LH RH LF RF0.25 0.25 0.25 0.25

An airline claims that 80% of adults have flown at least once. From a sample of 20 teenagers it is found that only 13 have flown at least once, giving reason to believe that the true parameter for teens is less than 80%. Let 0-7 represent having flown at least once (F) and let 8-9 represent never having flown (N). Using the table of random numbers provided, which gives the correct sequence of students in a simulated sample who have flown at least once (F) and who have not flown at least once (N)?

FNNFN FFNFF FFFFF FFFFF

This year, the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu.A partially completed tree diagram is shown. Fill in the indicated labels.Label 1 =Label 2 =Label 3 =Label 4 =Label 5 =

Flu shot flu no flu .30. 20

A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company's previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company's production line on a specific day. A golf pro takes the balls to the driving range and hits the 40 new-style golf balls first and then the 40 original-style golf balls. The distance each ball travels is recorded. At the end of the session, the mean distance traveled for the new type of golf ball was found to be significantly greater than the mean distance for the original-style golf ball. Which of the following is a valid conclusion?

Inferences can be made about all the golf balls produced on that day; however, a conclusion cannot be made that new-style golf balls travel farther than the original type of golf ball for this golf pro.

A florist wants to determine if a new additive would extend the life of cut flowers longer than the original additive. The florist selects the first 20 carnations from the ones recently delivered by the greenhouse and assigns the first 10 to the new additive and the rest to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy, and 2 carnations placed in the original additive still looked healthy. The proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive. Which of the following is a valid conclusion?

It cannot be inferred that the new additive caused the extended life of the cut flowers, and this inference cannot be applied to the carnations from the greenhouse.

Label 1: .18 Label 2: .15 Label 3: .35 Label 4: .32

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay). Which statement best explains the relationship between the variables shown?

More complex medical cases are often taken by larger hospitals, which increases the lengths of stay for larger hospitals.

A biology class conducted an experiment to determine whether playing classical music had an effect on the hatching rate of chicken eggs. Here are their results.Let event A = Music and event B = Hatched.Are events A and B independent?Yes, P(A) = P(A|B).Yes, P(A) = P(B|A).No, P(A) ≠ P(A|B).No, P(B) = P(B|A).

No, P(A) ≠ P(A|B).

A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1-10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A - B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot. Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. The tree diagram displays the possible outcomes of orders at this coffee shop.Which order is represented by label 1 in the tree diagram?Food itemNot food itemPlain coffeeNot plain coffee

Plain Coffee

The manufacturer of a soccer ball claims that only 3% of the soccer balls produced are faulty. An employee of this company examines the long-run relative frequency of faulty soccer balls produced as shown in the graph.Which conclusion can be drawn from this graph?The company's claim seems to be true because the graph shows that when 50 soccer balls were tested, only about 3% of them were faulty.We should not believe the company's claim that only 3% of their soccer balls are faulty because this graph shows a continuous increase in probability.Because the graph shows that the probability of producing a faulty soccer ball is 0.03, we can believe the company's claim that only 3% of the produced soccer balls are faultyThe graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company's claim that only 3% of the produced soccer balls are faulty.

The graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company's claim that only 3% of the produced soccer balls are faulty.

An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histogram below displays the lap times for Stefano, a runner in the 3,000-meter race. A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2. Which of the following is a true statement based on the histogram?

There were no lap times between 35 and 36 seconds.

The following two-way table shows another distribution of pets in a large apartment building.Suppose we select a resident of the apartment building at random.Let event A = Lizard and event B = Dog.Are events A and B independent?Yes, P(A) = P(A|B).Yes, P(A) = P(B|A).No, P(A) ≠ P(A|B).No, P(B) ≠ P(B|A).

Yes, P(A) = P(A|B).

Suppose that P(A) = 0.42, P(B) = 0.5, and P(A and B) = 0.21.Events A and BEvents A and B

are independent are not mutually exclusive

The following two-way table shows the distribution of pets in a large apartment building.Suppose we select a resident of the apartment building at random.Let event A = Cat and event B = Dog.Calculate and interpret P(B|A).The probability that a randomly selected resident owns a , given that the person also owns a , is equal to approximately 0.27 0.5190.90.

dog, cat, .519

Members of a charity organization are interested in finding ways to make it easier for individuals to donate money to their cause.They analyze the data from their last fiscal year of donations and find that 75% of their money came from online sources. Of the 60% of donations that came from regular donors (repeat donors), approximately 95% were submitted through the organization's website.Is the method of donation (online vs. not online) independent from the type of donor (regular vs. new) in this sample? yes no not enough information

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed, and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000 S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7% Using the computer output, what is the equation of the least-squares regression line?

ŷ = -7.611 + 0.186x

.07

A deli owner made a probability distribution chart for the meat choices of their customers' sandwiches when the sandwiches contain only one meat.HamTurkeyRoast BeefTunaSalami0.280.310.19?0.13What is the missing probability in the table?00.090.200.50

.09

.15

According to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. The Venn diagram displays the coffee preferences of the customers.A randomly selected customer is asked if they like hot or iced coffee. Let H be the event that the customer likes hot coffee and let I be the event that the customer likes iced coffee. What is the probability that the customer likes neither hot nor iced coffee?0.080.170.530.61

.17

What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter your answer as a decimal to the ten thousandths place.

.2273

A manager of a store determines that there is a 0.22 probability that a randomly selected customer who enters the store will make a purchase. If 20 customers enter the store and their decision to make a purchase is independent of the other customers' decisions, what is the probability that at least one of the customers makes a purchase?Round your answer to 3 decimal places.

.993

Grace rolls a fair, 6-sided die 50 times.What is the probability that she rolls at least one 6?Round your answer to 4 decimal places.0.00010.13890.33330.9999

.9999

Carlos thinks the traffic light to get out of his neighborhood is red more often than green. He decides to collect data to determine the probability of the light being red upon his approach. The graph of his long-run relative frequencies is shown.A graph titled Carlos apostrophe s red light has frequency on the x-axis, and probability on the y-axis. The graph levels out around y = 0.63.Which conclusion can be drawn from this graph?About half of the time, the traffic light is red when Carlos leaves his neighborhood.About 63% of the time, the traffic light is red when Carlos leaves his neighborhood.If the true probability that the traffic light is red when Carlos leaves his neighborhood is 0.63, there would be no variation in the graph.The probability that the traffic light is red when Carlos leaves his neighborhood cannot be determined from this graph because there is no pattern in a long series of traffic lights.

About 63% of the time, the traffic light is red when Carlos leaves his neighborhood.

Anna says there is a 0.15 probability that at least one of her shoes comes untied during her morning jogs.Which is the correct interpretation of this probability?When Anna jogs tomorrow morning, 15% of her shoes will come untied.If Anna jogs 100 mornings, then at least one shoe will come untied exactly 15 times.Fifteen percent of all joggers will experience a shoe that comes untied when they jog.If you take a very large sample of Anna's morning jogs, at least one shoe will come untied about 15% of the time.

If you take a very large sample of Anna's morning jogs, at least one shoe will come untied about 15% of the time.

A teacher claims that there is a 50% chance that she will collect homework for a grade on any given day. One week, she collected all five daily homework assignments. A student in this class is upset and explains that the teacher should not collect any homework assignments the following week in order to honor her 50% probability claim.Is the student's reasoning correct?Yes, the teacher should not collect homework assignments next week to bring the probability of homework being collected back to 0.5.No, if the teacher collects homework five days in a row, it is not possible for the probability of homework being collected to be 0.5.Yes, it is unlikely that the teacher would randomly collect homework assignments five days in a row, so not having a homework collection next week is due to happen.No, collecting homework and not collecting homework are equally likely in the long run, so whether or not the teacher collects homework on any single day cannot be determined.

No, collecting homework and not collecting homework are equally likely in the long run, so whether or not the teacher collects homework on any single day cannot be determined.

A certain dog can catch a properly thrown tennis ball with a probability of 0.95. Unfortunately, this dog has dropped the last six properly thrown tennis balls. The owner explains that the next throw has to be caught by the dog because he never misses this many. Is the owner's reasoning correct? No, the dog is on a losing streak, so he will drop the next ball thrown. Yes, the dog has missed the last six properly thrown tennis balls, so the next one thrown will be caught. No, the probability of the dog catching a properly thrown tennis ball is 0.95 over the long run, so the owner cannot say what will happen on the next throw. Yes, the dog catches 95% of properly thrown tennis balls, so the next one must be caught to compensate for the previous misses.

No, the probability of the dog catching a properly thrown tennis ball is 0.95 over the long run, so the owner cannot say what will happen on the next throw.

The following two-way table shows the distribution of a random sample of travelers and their preferences for accommodations and method of travel. Suppose a traveler is selected from this sample at random. Let event A = home sharing and event B = fly. Are events A and B independent?

Yes, P(A) = P(A|B).

Students must take an AP Sciences exam their senior year: 25% take AP Chemistry, 35% take AP Physics, 30% take AP Environmental Science and the remaining seniors take AP Biology. Of those who take AP Chemistry, 45% get accepted to their first-choice college, compared with 55% who take AP Physics, 20% who take AP Environmental Science, and 30% who take AP Biology.Use the partially completed tree diagram to fill in the indicated labels.Label 1 =Label 2 =Label 3 =Label 4 =Label 5 =

environmental science .10 1st choice .45 .55

.32

A large company states in their promotional literature that 80% of their employees have college degrees. If 5 employees are selected at random from this company, what is the probability that all 5 will have college degrees?0.00030.32770.67230.9997

.3277

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer vacuums their car?0.050.090.120.25

.25

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. The tree diagram displays the possible outcomes of orders at this coffee shop. Which probability is represented by label 4 in the tree diagram?

.30

Travel agents collected data from recent travelers about their modes of transportation for their vacations. They found that 37% traveled by airplane, 8% traveled by train, and 7% traveled by airplane and train. Let A be the event that the mode of travel was airplane and let T be the event that the mode of travel was train.What is the value of P(A and Tc), which is represented by 1 in the Venn diagram?0.080.300.370.62

.30

A recent survey found that 65% of high school students were currently enrolled in a math class, 43% were currently enrolled in a science class, and 13% were enrolled in both a math and a science class. Suppose a high school student who is enrolled in a math class is selected at random. What is the probability that the student is also enrolled in a science class?0.200.280.300.66

.20

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If three such number cubes are rolled, what is the probability that at least 1 of them shows a 2? 0.0006 0.2297 0.7703 0.9994

.2297

Laura buys an unfair coin online. The coin is supposed to land heads up 75% of the time. If this is true, what is the probability that in 20 flips, the first 15 land heads up and the last 5 land tails up?(0.75)(15)(0.25)(5)(0.75)15 + (0.25)5(0.75)15 (0.25)5(0.75)(15)+(0.25)(5)

(0.75)15 (0.25)5

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(M^C or C^C)?

.10

A survey of students at a large high school reveals that 59% of the students are studying a language other than English. The options for language study at the school include Spanish, French, Japanese, and American Sign Language (ASL). Currently, 6% of the students who study a language other than English are studying ASL.Suppose we select a student from the survey at random. Given that the student is studying a language other than English, what is the probability that the person is studying ASL?0.060.1020.4160.53

.102

Many of the students at a school play sports: 17% of students play soccer, 23% play football, and 48% of the football players play soccer. What is the probability that a randomly selected student plays both?0.08160.11040.47920.4800

.1104

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu.Use the tree diagram to determine the probability that a person with the flu is a person who received a flu shot.Enter your answer as a decimal to the ten thousandths place.

.1165

Executives for a company that prints logos on products are expanding the company's services to include souvenirs such as hats, shirts, and foam fingers for sports teams. The data they collected from a sample of 300 adults about their favorite sport to watch and their favorite souvenir to buy are shown in the table.A survey participant is randomly selected. Let F be the event that the participant prefers football and let N be the event that the participant prefers the foam finger. What is the value of P(F and N)?0.130.320.350.39

.13

Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color.What is the probability that a randomly selected participant dreams in black and white or color?0.060.070.130.26

.13

A high school math class has 28 students: 18 seniors and 10 juniors. What is the probability that four randomly selected students will be seniors?0.150.170.220.64

.15

A man owns five bow ties. He chooses one bow tie at random to wear on any given day. The polka-dot bow tie is his favorite, so his random process uses a larger probability for that bow tie. The rest of the bow ties are given equal probabilities of being chosen, as shown in the table. Polka Dot Stripes Checkered Argyle Paisley 0.40 ? ? ? ? What is the value of the missing probabilities? 0.15 0.20 0.25 0.60

.15

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. What is the probability that a randomly selected student studies for a test and gets a B or higher?0.080.110.330.55

.33

The probability that a student passes the AP Stats exam is 0.57. The probability that a student passes the AP Calculus exam is 0.43. The probability that a student passes the AP Stats exam given they passed the AP Calculus exam is 0.85. Find the probability that a student passes both exams.0.36550.48450.75441.3256

.3655

Executives for a car dealership are interested in the sales for the type of vehicle, SUV or truck, and the type of power train, two-wheel drive (2WD), four-wheel drive (4WD), or all-wheel drive (AWD). The data from the sales of 165 vehicles are displayed in the two-way table.A vehicle is randomly selected. Let S be the event that the vehicle is an SUV and let D be the event that the vehicle has 4WD. What is the value of P(S and DC)?0.040.230.380.41

.38

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student passes the test with a B or higher?

.41

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. The tree diagram displays the possible outcomes of orders at this coffee shop.Which probability is represented by label 3 in the tree diagram?0.440.560.650.70

.44

A researcher asked 520 randomly selected people of three different age groups (teen, young adult, and adult) about their favorite music genre. The two-way table displays the distribution of the responses.A participant is randomly selected. Let C be the event that the participant prefers country music and let T be the event that the participant is a teen. What is the value of P(Cc and Tc)?0.120.330.450.55

.45

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram. What is the probability that a randomly selected customer purchases the ultimate car wash if they vacuum their car?

.48

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu.What's the probability that a randomly selected adult got the flu?Enter your answer as a decimal to the ten thousandths place.

.5150

For students majoring in Hospitality Management, it was determined that 5% have visited 1-10 states, 16% have visited 11-20 states, 45% have visited 21-30 states, 19% have visited 31-40 states, and 15% have visited 41-50 states. Suppose a Hospitality Management student is picked at random. What is the probability that the student has not visited between 21 and 30 states?0.210.340.450.55

.55

Students must take an AP Sciences exam their senior year: 25% take AP Chemistry, 35% take AP Physics, 30% take AP Environmental Science, and the remaining seniors take AP Biology. Of those who take AP Chemistry, 45% get accepted to their first-choice college, compared with 55% who take AP Physics, 20% who take AP Environmental Science, and 30% who take AP Biology.Use the tree diagram to determine the probability that a student did not get into their first-choice college.Enter your answer as a decimal to the ten thousandths place.

.6050

Jocelyn boils 24 eggs. From experience, she knows that the shell of any given egg has a 0.04 probability of cracking during the boiling process. If shells crack independently, what is the probability that at least 1 egg will come out of the boiling process with a cracked shell?Round to 2 decimal places.

.62

A medical device company knows that 11% of patients experience injection-site reactions with the current needle. If 4 people receive injections with this type of needle, what is the probability that none of the 4 people get an injection-site reaction?0.00010.37260.44000.6274

.6274

.67

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.42. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. The probabilities are displayed in the tree diagram.What is the probability that Mrs. Barnes checks homework if the students take a pop quiz?0.250.330.670.77

.67

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.42. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. The probabilities are displayed in the tree diagram.What is the probability that Mrs. Barnes does not check homework if the students take a pop quiz?0.250.330.670.77

.67

.68

A recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. Suppose a pair of jeans is selected at random and it is determined that it has front pockets. What is the probability that a randomly selected pair of jeans with front pockets also has back pockets? 0.52 0.60 0.74 0.81

.74

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer purchases the classic car wash if they do not vacuum their car?0.260.350.540.75

.75

Emma has a fish tank with two fish in it. The probability that the first fish lives for at least one year is 0.84. The probability that the second fish lives for at least one year is 0.90. The lifespan of each fish is independent of the other fish.What is the probability that both fish live for at least one year? Do not round your answer.

.756

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.42. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. The probabilities are displayed in the tree diagram.What is the probability that the students will have a pop quiz on a randomly selected day?0.250.520.770.90

.77

.82

According to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. The Venn diagram displays the coffee preferences of the customers.A randomly selected customer is asked if they like hot or iced coffee. Let H be the event that the customer likes hot coffee and let I be the event that the customer likes iced coffee. What is the probability that a randomly selected customer likes hot or iced coffee?0.220.300.610.83

.83

A random sample of US adults revealed that approximately 68% own their own home. In this same sample, 52% of the respondents had completed some additional form of education following high school (trade or technical school, 2-year or 4-year college, military training, etc.). Finally, 44% of respondents had completed some additional form of education following high school and owned their own home.Given that a randomly selected adult from the survey has completed some additional form of education following high school, what is the probability that the person is a homeowner?0.440.6470.7650.846

.846

In a survey given by camp counselors, campers were asked if they like to swim and if they like to have a cookout. The Venn diagram displays the campers' preferences.A camper is selected at random. Let S be the event that the camper likes to swim and let C be the event that the camper likes to have a cookout. What is the probability that a randomly selected camper likes to have a cookout?0.040.890.930.99

.93

.981

A survey of teens suggested that 33% can name at least one professional baseball player, and 90% of those teens can also name at least one professional football player. In the entire population, 64% can name at least one professional football player. What percentage of teens can name at least one player from these sports? (0.33)(0.64) = 0.2112 0.33 + 0.64 = 0.97 0.33 + 0.64 - (0.33)(0.64) = 0.7588 0.33 + 0.64 - (0.90)(0.33) = 0.673

0.33 + 0.64 - (0.90)(0.33) = 0.673

A medical researcher claims that 60% of people with shellfish allergies do not have their first allergic reaction until adulthood. This value seems suspicious to a class of statistics students, so they ask an SRS of 30 adults with a shellfish allergy when they experienced their first allergic reaction. Fourteen of the adults experienced their first allergic reaction in adulthood. To see if this result is surprising, the class conducts a simulation to estimate the probability of obtaining a sample result as low as the one in their sample. Let 0-5 represent "adulthood" and 6-9 represent "before adulthood." Using the line of random numbers, how many "adulthood" responses are in the first trial of the simulation?

An animal researcher randomly selected 98 dogs and cats and recorded if they napped between 2:00 p.m. and 2:30 p.m. The two-way table displays the data.Suppose an animal is randomly selected. Let event C = cat and let event N = nap. What is the value of P(C|N)?

23/28

About 20% of the population experiences "cybersickness." This happens when the images in 3-D movies look so real they hinder the brain's ability to sort signals and cause people to get nauseated. To find out if this applies to teens, an SRS of 30 high school students was asked if they experience cybersickness. Eight students said "Yes." To see if this result is surprising, a simulation is conducted to estimate the probability of obtaining a sample result as high as this.Let 0-1 represent "Yes" and 2-9 represent "No."42188, 55736, 50953, 82496, 41985, 07738.Using the line of random numbers, how many "Yes" responses will there be in the first trial of the simulation?241526

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor a game console. A survey participant is randomly selected. Let M be the event that the participant brought a microwave and let C be the event that the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant brought both a microwave and a console, P(M and C)?0.650.710.760.90

????? (It is NOT .76)

A researcher randomly selects 165 vehicles and sees how many miles each car has been driven and the color of the vehicle. The two-way table displays the data. Suppose a vehicle is randomly selected. Let M = the vehicle has been driven many miles and B = the vehicle is blue.Which of the following is the correct value and interpretation of P(B|M)?P(B|M) = 0.36; given that the vehicle color is blue, there is a 0.36 probability that it has been driven many miles.P(B|M) = 0.36; given that the vehicle has been driven many miles, there is a 0.36 probability that the color is blue.P(B|M) = 0.54; given that the vehicle color is blue, there is a 0.54 probability that it has been driven many miles.P(B|M) = 0.54; given that the vehicle has been driven many miles, there is a 0.54 probability that the color is blue.

????? (NOT A)

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied if they do not pass the test with a B or higher?0.450.460.540.59

????? NOT .54

Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week's meeting. Which of the following represents the sample space for choosing a café for the first two weeks?R & G, R & B, G & R, G & B, B & R, B & GR & R, R & G, R & B, G & G, G & B, B & BR & R, R & G, R & B, G & R, G & G, G & B, B & R, B & G, B & BR & R, R & G, R & B, R & G, G & R, G & G, G & B, B & R, B & G, B & B

C R & R, R & G, R & B, G & R, G & G, G & B, B & R, B & G, B & B

In a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment. When considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60)(0.80) = 0.48. Is this student correct in his approach?Yes, these two events are most likely independent, so the joint probability can be found by multiplying the individual probabilities.No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.No, these two events are most likely not independent, so the joint probability cannot be found by multiplying the individual probabilities. They should be added instead.Yes, the joint probability can always be found by multiplying the individual probabilities.

No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.

Forty percent of the beads in a bag of more than 10,000 beads are yellow. Suzy pulls out 10 beads, one at a time with replacement, and notes that eight of these beads are yellow. She says the next bead pulled out will not be yellow because a yellow bead has been pulled out too many times in a row.Is Suzy's reasoning correct?Yes, it is unlikely that she would pull out so many yellow beads, so the next bead cannot be yellow.Yes, Suzy has correctly decided that more than 40% of the beads in this large bag are yellow.No, if a yellow bead is pulled 8 out of 10 times, the bag of beads is unfairly weighted toward yellow.No, it is true that the probability of pulling a yellow bead is 0.40, but Suzy should not expect that exactly 40% of such a small number of beads pulled will be yellow.

No, it is true that the probability of pulling a yellow bead is 0.40, but Suzy should not expect that exactly 40% of such a small number of beads pulled will be yellow.

A biology student wants to determine if using a fertilizer would help promote growth of new babies in spider plants. The student chooses 100 baby spider plants to be used in the study. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. Fifty of the plants will be given the fertilizer treatment and the other 50 plants will not receive any fertilizer. After one year, the shoots will be counted for each plant. Which of the following describes a completely randomized design for this experiment?

Number the plants 1-100 and put these numbers into a random number generator. The first 50 unique numbers generated will represent the plants placed in the fertilizer group. The remaining 50 plants will be placed in the group that does not receive fertilizer.

Josie believes that her mom calls her at the most inconvenient times. As a matter of fact, Josie thinks that 80% of the times that her mom calls, she is busy doing important tasks such as schoolwork, driving, or feeding the family pets. Which is the best interpretation of this probability? Josie's mom is calling her 80% of the day. If Josie is doing 10 important tasks in one day, her mom will call during 8 of those tasks. Josie has an 80% chance of completing her important tasks without her mom calling her. Over the course of many weeks, about 80% of the calls from Josie's' mom will come when she is busy doing important tasks.

Over the course of many weeks, about 80% of the calls from Josie's' mom will come when she is busy doing important tasks.

A contractor claims that she finishes a job on time 90% of the time. Last month, she only completed 7 out of her 10 jobs on time. To see if this is surprisingly low, a simulation was conducted 100 times under the assumption that she really does complete 90% of her jobs on time.The dotplot contains 100 trials of this simulation.A dotplot titled jobs completed on time has number of jobs completed on the x-axis, and frequency on the y-axis. 5, 1; 6, 3; 7, 15; 8, 26; 9, 45; 10, 11.Based on this dotplot and the sample of last month's on-time completions, which conclusion can be drawn?The contractor's true, on-time completion rate is only 50%.It is most likely that the contractor will complete about 9 out of 10 jobs.If we used a larger sample size of 40 jobs, the simulated dotplot would be different; therefore, we cannot draw a conclusion.The dotplot does not provide convincing evidence that her true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.

The dotplot does not provide convincing evidence that her true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.

An online news report claims that 50% of online news readers work in the business industry. To test this claim, a researcher takes an SRS of 25 online news readers. Nine of them work in the business industry. A simulation of 65 trials was conducted under the assumption that 50% of online news readers really do work in the business industry.A dotplot titled online readers and the business industry has number of readers from the food industry on the x-axis, and frequency on the y-axis. 8, 1; 9, 2; 10, 6; 11, 9; 12, 13; 13, 15; 14, 9; 15, 6; 16, 2; 17, 0; 18, 1; 19, 1.Based on this dotplot and the sample of 25 online news readers, which conclusion can be drawn?Since 0.36 of the sample works in the business industry, 0.36 is the true probability that an online news reader works in the business industry.It is most likely that, out of 25 online readers, between 12 and 13 work in the business industry.Because there appear to be outliers present that are greater than 16, we can conclude that more than 50% of online readers work in the business industry.There is about a 0.046 chance that 9 or fewer online readers work in the business industry. This is unusual and is convincing evidence that less than 50% of online readers work in the business industry.

There is about a 0.046 chance that 9 or fewer online readers work in the business industry. This is unusual and is convincing evidence that less than 50% of online readers work in the business industry.

A fitness expert claims that 25% of adults do not know how to swim. To test this claim, an SRS of 20 adults is taken. Two of the adults do not know how to swim. A simulation of 100 trials is conducted based on the assumption that 25% is the true probability that an adult does not know how to swim.A dotplot titled Nonswimmers has number of nonswimmers on the x-axis, and frequency on the y-axis. 1, 3; 2, 9; 3, 16; 4, 18; 5, 25; 6, 17; 7, 9; 8, 3; 9, 1.Based on the dotplot of the simulation results and the sample of 20 adults, which conclusion can be made?The actual probability that an adult cannot swim is only 12%.It is clear that exactly 5 out of 20 adults will be nonswimmers.If we continued to take more samples of 10 adults, the center of the distribution would shift to 2.There is about a 12% chance of 2 or fewer nonswimmers in a group of 20. This is not unusual and is not convincing evidence that the true probability that an adult cannot swim is less than 25%.

There is about a 12% chance of 2 or fewer nonswimmers in a group of 20. This is not unusual and is not convincing evidence that the true probability that an adult cannot swim is less than 25%.

A study reported that about half of high school seniors study for upcoming math tests. To find out if this applies to seniors at Garfield High School, an SRS of 30 seniors was asked if they study for their math tests. Nineteen responded "Yes."A dotplot is provided showing the results of 40 trials of this simulation.A dotplot titled seniors who study for math tests have number of seniors who responded yes on the x-axis, and frequency on the y-axis. 12, 2; 13, 5; 14, 6; 15, 11; 16, 9; 17, 4; 18, 2; 9, 0; 20, 1.Does this provide convincing evidence that seniors at Garfield High School study more than the report stated?No, there is an outlier at 20.No, there were outcomes as low as 12.Yes, only one trial had a result of 19 or larger.Yes, more than half of the simulated results are over 15.

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