Prob and Stats

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.

The stemplot below displays the grades (out of 30) that 26 students received on a quiz. Which of the following boxplots correctly displays the distribution of quiz grades?

A.

A researcher randomly selects 95 high school swimmers and asks them which swim stroke is their strongest and which bathing suit brand they prefer, brand A or brand B. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers brand B and F = the student's strongest stroke is freestyle. Which of the following is the correct value and interpretation of P(F|B)?

A. P(F|B) = 0.51; given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.

A computer's random number generator produces random integers from 1 to 50. What is the probability that the first 3 integers generated are single-digit numbers?

A. 0.0058

A random sample of adults was asked about their highest education level completed. The distribution of results is shown in the table. What is the probability that the highest level of education of an adult is a high school diploma, given that they have completed at least one of the education levels shown?

A. 0.04

Insurance company executives surveyed 200 young adults about their first motor vehicle. The results are shown in the two-way table. A survey participant is randomly selected. Let S be the event that the participant's first motor vehicle had six cylinders and let T be the event that the participant's first motor vehicle was a truck. What is the value of P(S and T)?

A. 0.06

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 only likes iced coffee?

A. 0.08

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?

A. 0.15

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?

A. 0.20

A study reported that about 40% of high school students have tried out for a sport at their school. To find out if this applies to Jessica's school, she surveyed an SRS of 20 students. Nine of them said that they had tried out for a sport. To see if this result is surprising, a simulation is to be conducted to estimate the probability of obtaining a sample result as high as this one. Let 0-3 represent students who tried out for a sport and 4-9 represent students who did not try out for a sport. Using the line of random numbers to run one simulation, what proportion of students tried out for a sport?

A. 0.40

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?

A. 0.44

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.8. 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. What is the probability that the students will have their homework checked and take a pop quiz on a randomly chosen day?

A. 0.48

A manufacturer of baseball hats claims that approximately 30% of people regularly wear baseball hats. From a random sample of 20 students at your school, you find that only four wear baseball hats regularly. This gives you reason to believe that the manufacturer's claim of 30% is too high. Let the digits 0-2 represent wearing a baseball hat (H) and the digits 3-9 represent not wearing a baseball hat (N). Use the table of random numbers to run one trial of this simulation. Which is the correct sequence of outcomes?

A. NNNNN HHNNN NNNHN NHNHNAnna 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?

Which of the following is an advantage of picking samples using stratified random sampling?

A. Stratified random sampling reduces sampling variability.

The following two-way table shows the distribution of high school students categorized by their grade level and music-listening preference. Suppose a high school student is selected at random. Let event A = junior and event B = earbuds. Are events A and B independent?

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

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?

A. ŷ = -7.611 + 0.186x

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.

A six-sided number cube is considered "loaded" if it is not fair. Which of the following could be the probability distribution for a loaded number cube?

B.

Some college advisors noticed the following breakdown of majors for the incoming freshman at their school: 3% math, 22% nursing, 16% psychology, 11% criminal justice, and 48% business. Suppose a first-year student was chosen at random. Which of the following is the probability distribution for that student's major?

B.

Ten people (labeled 1-10) have purchased raffle tickets for a fundraiser. However, they did not all purchase the same number of tickets. One ticket is to be selected at random. Which of the following could be the probability distribution for the winning ticket?

B.

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 S be the event that the participant prefers soccer and let T be the event that the participant prefers a T-shirt. What is the value of P(S and T)?

B. 0.03

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?

B. 0.05

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?

B. 0.09

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

B. 0.09

Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 6 such locations are generated, what is the probability that all 6 locations are in water?

B. 0.1281

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?

B. 0.17

A hair stylist knows that 87% of her customers get a haircut and 40% get their hair colored on a regular basis. Of the customers who get their hair cut, 24% also get their hair colored. What is the probability that a randomly selected customer gets their hair cut and colored?

B. 0.21

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(MC or CC)?

B. 0.29

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?

B. 0.30

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?

B. 0.3277

A teacher offers gift cards as a reward for classroom participation. The teacher places the gift cards from four different stores into a bag and mixes them well. A student gets to select two gift cards at random (one at a time and without replacement). Each outcome in the sample space for the random selection of two gift cards is equally likely. What is the probability of each outcome in the sample space?

B. 1/6

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?

B. 12.10%

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?

B. 2

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." Using the line of random numbers, how many "Yes" responses will there be in the first trial of the simulation?

B. 4

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?

B. 4.01

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. Which conclusion can be drawn from this graph?

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

Which of the following is not true about cluster sampling?

B. Cluster sampling has the advantage of reducing sampling variability.

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?

B. 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.

Shamir loves watching professional basketball. His favorite player, Freddy Rocket, successfully completes 85% of his free throws. During one game, Rocket misses his first four free throws. Shamir says that the next free throw has to be a success since Rocket rarely misses so many in a row. Is Shamir's reasoning correct?

B. No, the probability of Rocket making a free throw is 0.85 over the long run.

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?

B. 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.

A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave. The first six bats will be the control group, the second six will be treatment group 1, and the last six will be treatment group 2. Which component is missing from the biologist's process?

B. The biologist did not randomly assign the bats to the treatment groups.

The five-number summary of a data set is given below. Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20 Which of the following is a true statement about outliers for this distribution?

B. The distribution's minimum is an outlier.

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects' level of irritation was measured. Which of the following accurately describes the benefit of comparison in the experiment?

B. The level of irritation for both groups can be compared to see if the new cream had a significant effect.

A trade school would like to measure the long-term success of their graduates after they leave the school. The school emails a survey requesting information from graduates about their work experience. One question asks graduates to share their annual salary, and the results of the question will be shared in a brochure for incoming students. Is it likely that the survey results will provide an accurate estimate of mean annual salary for all of the school's graduates?

B. The survey will likely overestimate mean annual salary because those with higher salaries may be more likely to respond to the survey.

An observational study of suburban towns reveals that towns with more dedicated park land tend to have higher median home prices. A real estate agent suggests that a town's crime rate is a more accurate predictor of median home price. What is the confounding variable in this study?

B. the crime rate

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?

C. No, P(A) ≠ P(A|B).

A computer's random number generator produces random integers from 1 to 50. What is the probability that among the first 9 random integers generated, all of them fall in the range from 1 to 35?

C. (0.70)^9

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?

C. 0.13

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?

C. 0.33

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)?

C. 0.38

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)?

C. 0.45

On a certain hole, a golfer knows that he has a 70% chance of reaching the green (putting surface) in one stroke, 20% in two strokes, 8% in three, and 2% in four or more. If he reaches the green on his first stroke, he has an 80% chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30% chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke?

C. 0.56

A department store's survey suggests that 76% of shoppers buy food, 49% buy clothes, and 28% buy both food and clothes. Suppose a shopper is selected from the store at random and learn that they buy clothes. What is the probability that the shopper also buys food?

C. 0.57

A large company states in its promotional literature that 74% of its employees have college degrees. Assume this claim is true. If 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?

C. 0.5948

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?

C. 0.67

In a certain town, 65% of the voters support a school referendum up for a vote. If 5 voters are asked for their opinion, what is the probability that none of the 5 will support the referendum?

C. 0.8840

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)?

C. 0.90

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?

C. 0.93

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 Reese will get to pick the café for at least one of the first two weeks?

C. 5/9

Taylor's computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve. What percentage of numbers randomly generated by Taylor's computer is greater than 1.9?

C. 52.2%

A medical clinic is randomly selecting two staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 2 office staff. The nurses want to know the probability that both attendees will be nurses. The tree diagram displays the possible outcomes of randomly selecting two staff members. Which probability is represented by label 4 in the tree diagram?

C. 6/11

The stemplot displays 26 students' scores on a 90-point statistics test. The lowest possible passing grade on the test was a 54 out of 90. What percentage of students passed this test?

C. 77%

A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 120 people who snore participating in the experiment. Using a table of random digits, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison. How many unique random numbers need to be selected from the table of random digits?

C. 80

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)?

C. FNNFN FFNFF FFFFF FFFFF

According to a recent survey of first-year high school students, 28% chew gum daily. The students were also asked if they had recently gotten a cavity filled at the dentist. Of the 47% of first-year students who responded that they had a cavity recently filled, only 39% chewed gum daily. Is chewing gum independent of having a cavity filled recently?

C. No, P(Gum) ≠ P(Gum|Cavity).

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?

C. Plain Coffee

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?

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

A group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18-25): 1% use a cell phone that is 3 years or older, 2% use a cell phone that is 2-3 years old, 20% use a cell phone that is 1-2 years old, and 77% use a cell phone that is less than 1 year old. Suppose a young adult was selected at random. Let X equal the age of a randomly selected person's cell phone. Which of the following is the probability distribution for the age of that person's cell phone?

D.

According to a recent survey of adults, 38% say the almond is their favorite nut. The adults were also asked where they lived. Of the 19% of those who responded that they live in California, 40% chose the almond as their favorite nut. Is liking almonds independent of residency?

D. No, P(almond) ≠ P(almonds|California).

A computer's random number generator produces random integers from 1 to 50. What is the probability that at least one of the first 4 generated numbers is in the 20s?

D. 0.5904

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?

D. 0.6274

A recent survey of people who eat salad suggest that 78% like tomatoes on their salad, 49% like cheese on their salad, and 36% like both tomatoes and cheese on their salad. Suppose a person who eats salad is selected at random, and find they like cheese on their salad. What is the probability that the person also likes tomatoes on their salad?

D. 0.73

Sports science researchers determined that, of those people who skateboard, 22% have never had an injury, 45% have had one injury, 18% have had two injuries, and 15% have had three or more injuries. What is the probability that a randomly chosen skateboarder has not had three or more injuries?

D. 0.85

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If 4 such number cubes are rolled, what is the probability that at least 1 number cube will show a number 8 or larger?

D. 0.8842

A large company states in its promotional literature that 74% of its employees have college degrees. Assume this claim is true. If 4 employees are selected at random from this company, what is the probability that at least 1 of the selected employees has a college degree?

D. 0.9954

A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the probability that at least 1 of the selected marbles is blue?

D. 1-(17/29)^4

A local restaurant is having a contest in which patrons spin a wheel to win prizes. The wheel is divided into 10 identical segments, each marked with a different prize. Seven of the segments are labeled "Free Entrée" or "Free Appetizer." The other three are labeled "Free Valet Parking." Let the digits 0-6 represent winning free food and 7-9 represent winning valet parking. Using the line of random numbers, what is the best estimate of the number of free food prizes won by the next 20 patrons who spin the wheel?

D. 15

The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content lower than which value?

D. 194.9 mg

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)?

D. 23/38

A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 60 people who snore participating in the experiment who are labeled 01-60. Using a table of random digits, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison. Carry out the random assignment using the given selection from a table of random digits, starting with the first row and first column. Which list assigns the first eight people to the device 1 group?

D. 29, 17, 37, 48, 20, 27, 12, 23

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?

D. 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.

D. 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.

Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesses the color of the top card, looks at the card, and returns the card to the deck. The player continues to do this, shuffling the deck after each guess. Shawn has guessed the first three attempts as "blue" and has been correct on each guess. He says he will guess "yellow" for the next card since a yellow card is due to happen. Is Shawn's reasoning correct?

D. No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.

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. Based on this dotplot and the sample of 25 online news readers, which conclusion can be drawn?

D. 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.

D. 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 large city's transit department claims that only 10% of city buses run off schedule. To test this claim, a random sample of 10 buses is chosen at random. Five of the buses are running off schedule. To see how unusual this sample of buses is, a simulation of 100 trials was conducted under the assumption that 10% of the buses run off schedule. Based on the dotplot of the simulation results and the sample of 10 buses, which conclusion can be drawn?

D. There is about a 3% chance that 5 or more buses are running off schedule. This is unusual and is convincing evidence that the true probability that a bus is off schedule is more than 10%.

Suppose that among the 6,000 students at a high school, 1,500 are taking honors courses and 1,800 prefer watching basketball to watching football. If 450 students are both taking honors courses and prefer basketball to football, are the events "taking honors courses" and "preferring basketball" independent?

D. Yes, because

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 randomly selected. What is the probability that the student has visited 21 or more states?

MAYBE: D. 0.79

A student has heard that spinning pennies on a table, rather than flipping them in the air, results in tails side up 65% of the time. If this is true, what is the probability that a student who spins 4 pennies will have at least one land heads side up?

NOT 0.0150

In a certain town, 65% of the voters support a school referendum up for a vote. If 5 voters are asked for their opinion, what is the probability that at least 1 of the 5 will not support the referendum?

NOT 0.1160

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?

NOT 0.75

A recent survey has shown that 68% of professional photos are of humans, 39% are of pets, and 17% are of both humans and pets. Suppose a professional photo is selected at random and it is of a human. What is the probability that the photo also has a pet?

NOT A. 0.17 NOT C. 0.39

A researcher randomly sampled 222 high school students to determine their favorite color and whether or not they played a sport. The two-way table displays the data. A randomly selected student who participated in the survey is selected. Let event S = the student plays a sport and let event B = favorite color is blue, green, or purple. What is the value of P(B|S)?

NOT B. 41/118 NOT C. 36/77

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)?

NOT C 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.

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?

NOT C. 0.54

A student has heard that spinning pennies on a table, rather than flipping them in the air, results in tails side up 65% of the time. If this is true, what is the probability that a student who spins 4 pennies will have them all land tails side up?

NOT C. 0.8215

A recent survey suggests that 47% of all televisions are connected to the internet, 32% are voice controlled, and 22% are both connected to the internet and voice controlled. Suppose a television is selected at random and it is voice controlled. What is the probability that a randomly selected voice-controlled television is also connected to the internet?

NOT: B. 0.47 NOT D. 0.79 MAYBE: C. 0.69

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)?

NOT: D. 0.90

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.

The scatterplot illustrates the relationship between two quantitative variables. The relationship in the scatterplot is

positive and linear with no unusual points.