U1 stats

A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below. The cafeteria should budget $_____ on average for one gallon of milk.

2.90

There are four blood types, and not all are equally likely to be in blood banks. In a certain blood bank, 49% of donations are Type O blood, 27% of donations are Type A blood, 20% of donations are Type B blood, and 4% of donations are Type AB blood. A person with Type B blood can safely receive blood transfusions of Type O and Type B blood. What is the probability that the 4th donation selected at random can be safely used in a blood transfusion on someone with Type B blood?

A. (0.31)^3(0.69)

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Students who receive a 3 or higher can earn college credit. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. Which of the following histograms correctly displays the distribution?

A. (graph)

In a certain town, 45% of the voters support a school referendum up for a vote. Sharon will ask people about why they support the referendum, but she needs to find people who support it. What is the probability that it takes 7 people to find the first person who supports the referendum?

A. 0.0126

Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of $4.10. Assume that D and L are independent random variables. What is the probability that Lynnetta will earn more than $110 in a randomly selected week?

A. 0.034

The owner of an apple orchard has learned from previous experience that, on average, 5% of the harvested apples have blemishes. The owner randomly selects 10 apples from this year's harvest. What is the probability that 2 of the apples have blemishes?

A. 0.07

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 the first white marble chosen is on the 4th selection?

A. 0.1032

A bottled water company runs a promotion in which 1 out of every 5 bottles has the word "Winner" printed under the cap. Winners receive a free bottle of water. A store owner notices that in the last 8 bottles of water purchased, 3 have been winners. What is the probability of getting 3 "Winner" caps on 8 bottles of water?

A. 0.15

Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the standard deviation of the distribution?

A. 1.39

At a carnival, a customer notices that a prize wheel has 5 equal parts, one of which is labeled "winner." She would like to conduct a simulation to determine how many spins it would take for the wheel to land on "winner." She assigns the digits to the outcomes. 0, 1 = winner 2-9 = not a winner Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many spins does it take until the first prize is won?

A. 2

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. What is the median of the distribution? 2 2.1 2.5 3

A. 2

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X be the value of a random spin. The distribution of X is given in the table. What is the standard deviation of the distribution?

A. 3.01

Which statement below correctly depicts the expected value of a fair game?

A. E(X) = 0

Hannah and Claire each have a chicken coop with 6 hens. Let H represent the total number of eggs the hens lay on a randomly chosen day in Hannah's coop and let C represent the total number of eggs the hens lay on a randomly chosen day in Claire's coop. The two distributions are displayed in the table and histograms. Which statement correctly compares the centers of the distributions?

A. Hannah's hens appear to lay more eggs, on average, than Claire's hens.

Mrs. Bready has a large bag filled with red and green cards. She tells the class that 15% of the cards are red and 85% are green. At the end of each class, she mixes the cards, reaches inside the bag, and draws out one card at random. If a red card is drawn, the students will not be assigned homework. She shows the class the card, and then places the card back in the bag. Carla would like to carry out a simulation to estimate the number of days it will take in order to get a "no homework" day. What is an appropriate assignment of digits?

A. Let 00-14 = red. Let 15-99 = green.

A produce manufacturer fills bags of baby carrots by weight. Each bag is supposed to have 12 ounces of baby carrots. Unfortunately, 3% of the baby carrots are discolored. Let X represent the number of discolored baby carrots in a bag. Are the conditions for a binomial setting in this scenario met?

A. No, there is no fixed number of baby carrots.

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. Which of the following correctly represents the probability of a randomly selected purchase having at most three tickets?

A. P(X ≤ 3)

An outboard motor on a boat has a cord to pull to start it. Advertisements boast that the motor "Starts on the first pull, every time!" In reality, the motor has a 95% chance of starting on each pull. A customer wants to know how many times he will have to pull the cord to start the motor. Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

A. Yes, the geometric distribution is appropriate.

A certain airline has a 90% probability that its flights are on time. Fifteen of this airline's flights leave the local airport each day. Let X represent the number of flights that are on time each day. Assuming flights are on time independently of one another, what is the shape of the probability histogram of X?

A. skewed left

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table. Which of the following histograms correctly displays the distribution?

B. (graph)

Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll?

B. -1/6

A large company boasts in their promotional literature that 74% of their employees have college degrees. Assume this claim is true. What is the probability that if people are selected at random from this company, that the first person to have a college degree is the 3rd person selected? 0.0176 0.0500 0.4052 0.9824

B. 0.0500

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the probability that an injection-site reaction occurs for the first time on the 6th patient of the day? 0.0001 0.0614 0.3685 0.4970

B. 0.0614

The weight of panda bears, P, is approximately Normally distributed with a mean of 185 pounds and a standard deviation of 12.3 pounds. The weight of koala bears, K, is approximately Normally distributed with a mean of 21.5 pounds and a standard deviation of 4.8 pounds. Suppose a zookeeper randomly chooses a panda and a koala bear, where P and K are independent random variables. What is the probability that the total weight for the two animals is 225 pounds or more?

B. 0.081

A computer technician notes that 40% of computers fail because of the hard drive. If he repairs many computers a day, what is the probability that the first computer that has failed due to the hard drive is his 4th computer of the day?

B. 0.0864

At a manufacturing plant, it is known that 8% of the computer chips produced are defective. A random sample of 20 chips is taken. What is the probability that 3 of those chips are defective?

B. 0.14

At West High School, 10% of the students participate in sports. A student wants to simulate the act of randomly selecting 20 students and counting the number of students in the sample who participate in sports. The student assigns the digits to the outcomes. 0 = student participates in sports 1-9 = student does not participate in sports Here is a portion of a random number table. In the first trial, line 1, two of the 20 digits are zeros, meaning that two of the 20 selected students participate in sports. Starting at line 2 and using a new line for each trial, carry out 4 more trials to determine the number of students who participate in sports in random samples of size 20. In what proportion of all 5 trials do we find that 0 students participate in sports?

B. 0.2

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table. What is the probability that the basketball player will make six free throws out of the eight attempts?

B. 0.21

Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S - T. What is the probability that Soledad sends more texts on a randomly selected day?

B. 0.214

A basketball player makes 85% of her foul shots. If 10 of her foul shots are randomly selected, what is the probability that 8 of them are successful shots?

B. 0.28

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student. What is the probability that a randomly selected student got a B?

B. 0.31

A construction company has two divisions: ceilings and floors. The amount of revenue for the ceiling division, C, is approximately Normally distributed with a mean of $2.6 million per year and a standard deviation of $0.9 million per year. The amount of revenue for the flooring division, F, is approximately Normally distributed with a mean of $3.1 million per year and a standard deviation of $1.1 million per year. Assume C and F are independent random variables. What is the probability that the ceiling division makes more revenue than the flooring division in a randomly selected year?

B. 0.363

A volleyball player's serving percentage is 75%. Six of her serves are randomly selected. Using the table, what is the probability that at most 4 of them were successes?

B. 0.466

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. What is the standard deviation of the distribution?

B. 0.95

A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table. What is the standard deviation of the distribution?

B. 1.40

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. What is the mean of the distribution? 2.5 2.95 3 3.5

B. 2.95

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. What is the median of the distribution?

B. 3

In a certain board game, a 12-sided number cube showing numbers 1 through 12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears. What is the probability that the first such number is on the 3rd roll?

B. 4/27

Consider the given probability histogram of a binomial random variable. What are the center and shape of the distribution?

B. Center: 2.5 Shape: symmetric

Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?

B. It is a favorable game.

A computer technician notes that 40% of computers fail because of the hard drive, 20% fail due to the processor, 15% of problems are with the keyboard, and 5% of problems are due to something else. What is the mean of the number of computers he will work on before seeing his first computer that has failed because of the hard drive?

B. Since 40% is equivalent to 2/5 , it is expected that 5/2 = 2.5 computers until one has failed due to the hard drive.

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. Which statement correctly interprets the standard deviation?

B. The grade for a randomly selected student would typically vary from the expected grade by 1.08.

There are 10 multiple-choice questions on a math quiz. Each question has four answer choices with one correct answer. Let X represent the number of questions answered correctly for a student who is randomly guessing each answer choice. Have the conditions for a binomial setting been met for this scenario?

B. Yes, all four conditions in BINS have been met.

The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament, and the games are played independently of one another. Let X represent the number of games the team might win in this tournament. What are the mean and standard deviation of X?

B. mean = 3.48; standard deviation = 1.21

According to a website, one out of five adults will make an online purchase in any given week. A survey asked 20 randomly selected adults if they had made an online purchase within the past week. Let X represent the number of adults who had made an online purchase within the past week. What is the shape of the probability histogram of X?

B. skewed right

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is displayed in the histogram. What is the shape of this histogram?

B. skewed right

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament?

C. $2,600

The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lunch each day. What is the expected value for a student to spend on lunch each day?

C. $5.18

A shipping company claims that 90% of its packages are delivered on time. Jenny noticed that out of the last 10 packages shipped, 2 were late. What is the probability that 2 out of 10 randomly selected shipments would be late?

C. 0.19

A statistics teacher decides to give his students a 5-question multiple-choice quiz with 4 possible answers for each question. If a student decides to randomly guess on each question, what is the probability the student will get 2 questions correct?

C. 0.26

A couple is thinking about having 3 children. Assume that each child is equally likely to be a girl or a boy. What is the probability that exactly 2 of the children are girls?

C. 0.375

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. What is the probability of earning a score lower than 3?

C. 0.38

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. What is the probability of earning a score of 3 or higher?

C. 0.62

The probability of an archer hitting her target is 83%. Suppose she has 20 shots to take, and each shot is independent of the others. Let X represent the number of targets hit. What is the mean of X?

C. 16.6

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 standard deviation of X, the number of draws until the first red marble?

C. 2.0770

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X represent the value of a spin. The distribution of X is given in the table. What is the expected value of the distribution? 1 1.5 2.1 3.5

C. 2.1

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. What is the mean of the distribution? 2 3 2.98 3.50

C. 2.98

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. What is the median of the distribution?

C. 3

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the median of the distribution? 3 3.5 4 4.2

C. 4

At a certain pizzeria, it is known that 12% of orders are for extra-large pizzas. What is the expected number of pizzas that will be ordered until the first extra-large pizza is ordered?

C. 8.33 pizzas

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score?

C. 90.8

Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

C. A number less than or equal to 3 will add one point. A 4 will lose two points.

A coin is flipped 25 times, and we would like to know the probability that 15 or more of those flips are heads side up. Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

C. No, because it is not looking for the first occurrence of success.

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student. Which of the following correctly represents the probability that a randomly selected student has a grade higher than a C?

C. P(X > 2)

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject's standardized tests are displayed in the table and the histograms. Which statement correctly compares the centers of the distributions? A. The center for the distribution of scores appears to be lower for subject B than for subject A. B. The center for the distribution of subject A is approximately 3, while the center for subject B is approximately 4. C. The center for the distribution of scores appears to be higher for subject B than for subject A. D. The center for the distribution of scores appears to be about the same for both subjects.

C. The center for the distribution of scores appears to be higher for subject B than for subject A.

A hotel has two different ice machines that fill buckets of ice independently of each other. Let A represent the amount of ice in a bucket filled by machine A, and let B represent the amount of ice in a bucket filled by machine B. Which of the following choices explains the meaning of independent random variables in context?

C. The independence of the two ice machines means that knowing how much one machine fills does not help us predict how much the other fills.

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. Which is the correct interpretation of the standard deviation?

C. The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.4 eggs.

Elroy enjoys roller skating and weight training. Let X represent the number of hours he spends roller skating weekly, and let Y represent the number of hours he spends weight training weekly. The mean of X is 5 hours, and the mean of Y is 7 hours. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

C. mean=12; Elroy can expect to roller skate and weight train, on average, 12 hours in a typical week.

Randi and Leah are studying together for an exam. Let X represent the number of hours Randi spends studying nightly, and let Y represent the number of hours Leah spends studying nightly. The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours. Assuming these are independent random variables, which answer choice correctly calculates and interprets the standard deviation of the sum, S = X + Y?

C. mean=2.1; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.

There are frogs and koi in a pond, and the number of frogs and the number of koi in the pond are independent. Let X represent the number of frogs in any given week, and let Y represent the number of koi in any given week. X has a mean of 28 with a standard deviation of 2.7, and Y has a mean of 15 with a standard deviation of 1.6. Which answer choice correctly calculates and interprets the standard deviation of the difference, D = X - Y?

C. mean=3.1; this pond can expect the difference of frogs and koi to vary by approximately 3.1 from the mean.

A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are $100 each, what is the profit per item?

C. profit of $2.90

A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent.

D. $3.70

71% of the surface of the Earth is covered in water. A random number generator uses latitude and longitude to select a random location on Earth. If such locations are generated, what is the probability that the first of those locations that is over land is on the 8th location? (0.29)8 (0.71)8 (0.29)7(0.71) (0.71)7(0.29)

D. (0.71)^7(0.29)

A quarterback's pass-completion percentage is 70%. Eight of his passes are randomly selected. What is the probability that 6 of them were successful passes?

D. 0.30

Claire flips a coin 6 times. What is the probability that the coin will show tails 3 times?

D. 0.313

A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line. Assuming that field goal attempts can be considered random events, what is the probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line?

D. 0.39

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table. What is the probability that the value is at most 2?

D. 0.8

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student. What is the probability that a randomly selected student earned a C or better?

D. 0.91

Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at least once?

D. 0.94

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the mean of the distribution? 3 3.5 4 4.2

D. 4.2

There are four blood types, and not all are equally likely to be in blood banks. In a certain blood bank, 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A blood bank wants to know how many donations will be required, on average, to achieve at least one of each of the blood types. Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

D. No, since a success and failure on each trial cannot be defined.

Ian shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the number of aces he observes. Have the conditions for a binomial setting been met for this scenario?

D. No, the cards are not being replaced, so the independence condition is not met.

In a game of darts, there are 20 sectors on a target, and a smaller circular "bullseye" in the center. In this particular game, a player must correctly call "low," consisting of the sectors numbered 1-10; "high," consisting of the sectors numbered 11-20; or "bullseye," depending on what they are trying to hit. If they hit the section they call, they are a winner. A player will attempt to hit "low" on the first throw, then will attempt to hit "high" on the second throw, then will attempt to hit "bullseye" on the third throw, and so on until hitting the section they called. Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

D. No, the probability of success is not the same for each of the trials.

Tonya and Emily each have an online jewelry store. Let T represent the amount of money Tonya earns daily, and let E represent the amount of money Emily earns daily. The mean difference, D = T - E, of the amount of money that Tonya and Emily earn on a typical day is $312. What is the correct interpretation of this value?

D. On average, Tonya makes $312 more than Emily on a typical day.

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 expected number of draws until the first red marble?

D. Since 11/29 of the marbles are red, 29/11 draws are expected until a red marble is drawn.

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. Which of the following is the correct interpretation of P(X > 4)?

D. The probability of a randomly selected test having a score higher than 4 is 0.15.

A clothing store manager notices that when any one customer comes into the store, there is a 52% chance they will make a purchase. She also notices that one customer's decision to make a purchase is independent of other customers' decisions. Suppose one Friday, 75 customers come into this store. Let X represent the number of customers who make a purchase. What is the shape of the probability histogram of X?

D. approximately symmetric

A coin is weighted so that the probability of getting heads is (2/3). Suppose you toss this coin 15 times. Let X represent the number of heads. What are the mean and standard deviation of X?

D. mean = 10; standard deviation = 1.83

JT has two jobs. He mows yards and washes cars in his neighborhood. Let X represent the amount of weekly earnings for mowing yards, and let Y represent the amount of weekly earnings for washing cars. The mean of X is $60, and the mean of Y is $35. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

D. mean=95; JT can expect to earn $95, on average, in a typical week.

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Students who receive a 3 or higher can earn college credit. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is displayed in the histogram. What is the shape of the distribution?

D. unimodal, approximately symmetric

A baseball player has a hitting average of 0.325. If seven at-bats are randomly selected, what is the probability of getting 4 hits? 0.01 0.02 0.08 0.12

NOT C

The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 6 hens. Using the table, what is the probability that at least 2 of the hens will lay eggs on a given day? 0.015 0.017 0.983 0.998

NOT C, maybe D. 0.998