stats

Amy has 12 brown golf tees, 8 white golf tees, 10 red golf tees, 6 blue golf tees, and 12 green golf tees in her golf bag. If she selects one of the tees from the bag at random, what is the probability that she selects a tee that is not brown or blue? A- 3/8 B- 5/8 C- 21/32 D- 3/4 E-7/8

B

The random variable K has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of random variable K ? a- 4 b- 240 c- 0.9375 d- 0.0625 e- 15.49

e mean= 1/p so p= 16 sd= (√1-(1/16))/(1/16) = 16√(15/16)= 15.49

A high school theater club has 40 students, of whom 6 are left-handed. Two students from the club will be selected at random, one at a time without replacement. What is the probability that the 2 students selected will both be left-handed? a- 30/15600 b- 30/1600 c- 6/40 d- 36/1600 e- 1156/1600

a 6/40 * 5/39 ,,, 6*5= 30 40*39= 15600 so 30/15600

At a local elementary school, 35 percent of all students have brown eyes, 45 percent have brown hair, and 60 percent have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event that the selected person has brown eyes, and let H represent the event that the selected person has brown hair.Are E and H mutually exclusive events? A- Yes, because P(E∩H)=0 B- Yes, because P(E∩H)=0.2 C- Yes, because P(E∩H)=0.6 D- No, because P(E∩H)=0.2 E- No, because P(E∩H)=0.6

D

In the United States, the generation of people born between 1946 and 1964 are known as baby boomers, and the generation of people born between 1981 and 1996 are known as millennials. Currently, 18 percent of the population are baby boomers and 27 percent of the population are millennials. A random sample of 500 people will be selected. Let the random variable B represent the number of baby boomers in the sample, and let the random variable M represent the number of millennials in the sample. By how much will the mean of M exceed the mean of B ? a- 225 b- 90 c- 9 d- 135 e- 45

e (500*.27)-(500*.18)

According to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. A random sample of 20 employed young adults will be selected. What is the probability that 8 of the selected young adults will expect to bring work on a vacation trip? (20 8) (___)^8 (____)^12

(20 8) (.74)^8 (.26)^12

Consider rolling two number cubes, each of which has its faces numbered from 1 to 6. The cubes will be rolled and the sum of the numbers landing face up will be recorded. Let the event E represent the event of rolling a sum of 5. How many outcomes are in the collection for event E ? Responses Five Two One Six Four

4

According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W ? a- 16.79 b- 4.24 c- 16.92 d- 4.11 e- 0.24

d

For the lunch special at a high school cafeteria, students can get either salad or french fries as a side order. The following table shows the number of each side order for the lunch specials purchased on one day, classified by the grade of the student. grade: 9 | 10 | 11 | 12 | total salad: 37 | 34 | 21 | 28 | 120 fries: 83 | 71 | 57 | 37 | 248 total: 120 | 105 | 78 | 65 | 368 From those who purchased the lunch special that day, one student will be selected at random. What is the probability that the student selected will be in grade 10 given that the student ordered french fries as the side order? a- 71/368 b- 248/368 c- 71/105 d- 71/248 e- 105/368

d given that they ordered fries means denominator is 248 and 71 10th graders ordered fries so 71/248

A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram. Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed? 0.28 0.91 0.72 0.09 0.19

.28

Past records indicate that 15 percent of the flights for a certain airline are delayed. Suppose flights are randomly selected one at a time from all flights. Assume each selection is independent of another. Which of the following is closest to the probability that it will take 5 selections to find one flight that is delayed? A- 0.0783 B- 0.0921 C- 0.4780 D- 0.5220 E- 0.5563

a

The random variable W can take on the values of 0, 1, 2, 3, or 4. The expected value of W is 2.8. Which of the following is the best interpretation of the expected value of random variable W? a- For values of w repeatedly selected at random from the distribution, the mean of the selected values will approach 2.8 b- a value of w randomly selected from the distribution will be away than 2.8 units from the mean c- the mean of a random variable sample of values selected from the distribution will be 2.8 d - a randomly selected value of w must be equal to 2.8 e- the values of w will vary about 2.8 units from the mean of the distribution

a

In the United States, 75 percent of adults wear glasses or contact lenses. A random sample of 10 adults in the United States will be selected. Which of the following is closest to the probability that fewer than 8 of the selected adults wear glasses or contact lenses? a- 0.28 b- 0.10 c- 0.47 d- 0.53 e- 0.76

c

A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.Which of the following is the best interpretation of the probability 0.20 ? A- For all workers in the United States, 20% will work in finance. B- For all finance workers, 20% will have a tattoo. C- For all people with tattoos, 20% will work in finance. D- For a specific group of 5 finance workers, 1 will have a tattoo. E- For a specific group of 5 people with a tattoo, 1 will work in finance.

B

A business journal reports that the probability that Internet users in the United States will use a mobile payment app is 0.60. The journal claims this indicates that out of 5 randomly selected Internet users, 3 will use the mobile payment app.Is the business journal interpreting the probability correctly? A- No, because the Internet users are not independent of each other. B- No, because only 60% of all people use the Internet. C- No, because 0.60 represents probability in the long run for many Internet users. D- Yes, because Internet users are selected at random. E- Yes, because 3 out of 5 is equal to 60%.

C

A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.Which of the following is the best interpretation of the probability that one spin of the spinner will land in a shaded sector? A- For many spins, the long-run relative frequency with which the spinner will land in a shaded sector is 1/3. B- For many spins, the long-run relative frequency with which the spinner will land in a shaded sector is 1/2. C- For many spins, the long-run relative frequency with which the spinner will land in a shaded sector is 2/3. D- For 6 spins, the spinner will land in a shaded sector 4 times. E- For 6 spins, the spinner will land in a shaded sector 2 times.

C

Let the random variable X represent the number of people living in a household in a certain town. The standard deviation of X is 1.8. Which of the following statements is the best interpretation of the standard deviation? a- On average, the number of people living in a household varies from the mean by about 1.8 people. b- For a random sample of households, the average number of people per household will be 1.8 people away from the mean. c- The number of people living in a randomly selected household will be 1.8 people away from the mean. d- The number of people living in a randomly selected household is expected to be 1.8 people. e- For a random sample of households, the average number of people per household is expected to be 1.8 people.

a

The students at a certain high school have an elective period, where each student chooses an elective from among four options. The following table shows the number of students who selected each elective for the 1,500 students at the high school. Art: 385 Music: 365 Physical Education:380 Engineering: 370 Total: 1,500 One student from the school will be selected at random. What is the probability the selected student chose the art elective and the music elective? a- 0 b- 750/1500 c- 385/1500 d- 365/750 e- 385/750

a because they can only choose one

During a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. Suppose 20 electrical transformers are randomly selected from the population. Let the random variable T represent the number of electrical transformers operating during a severe storm. Which of the following is the best interpretation of the random variable T ? A- It is a binomial variable with mean 17 transformers and standard deviation √2.55 transformers. B- It is a binomial variable with mean 17 severe storms and standard deviation √2.55 severe storms. C- It is a binomial variable with mean 0.85 transformer and standard deviation 20 transformers. D- It is a variable that is not binomial with mean 17 transformers and standard deviation√2.55 transformers. E- It is a variable that is not binomial with mean 0.85 severe storm and standard deviation 20 severe storms.

a sq rt npq

The following table shows the probability distribution for the prize amounts that will be awarded at a school raffle. Prize 1 | 5 | 10 | 20 | 50 Probability .6 | .3 | .05 | .04 | .01 Let the random variable P represent a randomly selected prize amount. What is the expected value of P ? a- 17.20 b- 4 c- 1 d- 10 e- 3.90

e

A consumer group is investigating the number of flights at a certain airline that are overbooked. They conducted a simulation to estimate the probability of overbooked flights in the next 5 flights. The results of 1,000 trials are shown in the following histogram. (0: .007, 1: .049, 2: .181, 3: .317, 4: .332, 5: .114) Based on the histogram, what is the probability that at least 4 of the next 5 flights at the airline will be overbooked? a- 0.114 b- 0.446 c- 0.500 d- 0.332 e- 0.886

b

A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ? A- A binomial variable with 15 independent trials B- A binomial variable with 25 independent trials C- A variable that is not binomial with 25 independent trials D- A binomial variable with 40 independent trials E- A variable that is not binomial with 40 independent trials

b

Julio sells computers at an electronics store. Let the random variable C represent the number of computers that Julio sells in one week. The following table shows the probability distribution of C. c 0 1 2 3 4 5 6 P(C=c) 0.04 0.08 0.16 0.21 0.30 0.18 0.03 Julio earns $800 per week, with a commission of $200 per computer sold. What is the expected value of Julio's earnings for one week? a- $662 b- $1,462 c- $3.31 d- $3,310 e- $2,848

b

Question In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population? a- Let the digits from 0 to 2 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches. b- Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches. c- Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches. d- Let the digits 0 and 1 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches. e- Let the even digits represent birds with a wingspan greater than 10 inches and the odd digits represent birds with a wingspan less than or equal to 10 inches.

b

The random variable X takes on the values of 2, 5, n, and 15. The probability distribution of X is shown in the following table. X: 2 | 5 | n | 15 P(x): .1 | .4 | .2 | .3 The expected value of X is 9.1. What is the value of n ? a- 10 b- 8.52 c- 14.4 d- 8 e- 12

e

A representative from a company that manufactures items for left-handed people will attend a large convention. The representative hopes to find a left-handed person at the convention to try out the items. The representative will select an attendee at random until a left-handed person is found. Assume each selection is independent of another. If 10 percent of the convention attendees are left-handed, what is the probability that the representative must select 4 attendees to find one who is left-handed? a- 0.9(0.1^4) b- 0.9(0.1^3) c- .1(0.9^3) d- 0.1(0.9^4) e- 0.12(0.9^2)

c

At Mike's favorite coffee shop, the coffee of the day is either a dark roast, a medium roast, or a light roast. From past experience, Mike knows that the probability of the coffee being a light roast is 0.15 and the probability of the coffee being a dark roast is 0.25. What is the probability of the coffee of the day not being a light roast or a dark roast on the next day that Mike visits the coffee shop? a- 0.40 b- 0.85 c- 0.60 d- 0.25 e- 0.15

c

At a certain restaurant, 35 percent of the customers order the daily special each day. Assume that each day the customers arrive randomly and order independently. Let the random variable X represent the number of orders placed until the first daily special is ordered. The distribution of X is geometric and has an expected value of approximately 2.86. Which of the following is the best interpretation of the expected value? a- For a random sample of the days, the average number of orders of the daily special will be 2.86. b- Each day, the ratio of the number of orders of the daily special to the number of orders of other menu items is about 2.86 to 1. c- Over many days, it takes about 2.86 orders, on average, to be placed until the first daily special is ordered. d- Each day, 3 customers will order the daily special. e- Over many days, the average number of customers ordering the daily special is approximately 2.86.

c

At a large university, data were collected on the number of sisters and brothers that each student had. Let the random variable X represent the number of sisters and the random variable Y represent the number of brothers. The distribution of X has mean 1.00 and standard deviation 0.94. The distribution of Y has mean 1.07 and standard deviation 1.04. What is the mean of the distribution of X+Y ? a- 2.04 b- 2.01 c- 2.07 d- 1.98 e- 2.0528

c

Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected? a- {oatmeal, coffee, pancakes, eggs, tea} b- {(oatmeal, eggs, pancakes), (coffee, tea)} c- {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)} d- {(coffee, tea, oatmeal), (coffee, tea, eggs), (coffee, tea, pancakes)} e- {(oatmeal, pancakes), (oatmeal, eggs), (eggs, pancakes), (coffee, tea)}

c

Let random variable Q represent the number of employees who work at a certain restaurant on a given day. The following table shows the probability distribution of the random variable Q. Number of EmployeesProbability 20- 0.1 | 21- 0.1 | 22- 0.1 | 23- 0.4 | 24-0.3 Which of the following claims is best supported by the table? a- The most likely number of employees who work on a given day is 24. b- The mean number of employees who work on a given day is less than the median number of employees who work on a given day. c- The mean number of employees who work on a given day is greater than the median number of employees who work on a given day. d- The mean number of employees who work on a given day is equal to the median number of employees who work on a given day. e- On a given day, the number of employees who work at the restaurant occurs with equal probabilities.

c

Approximately 9 percent of the residents of a large city have seen a certain theater production that is currently playing in the city. A marketing researcher will randomly select residents until one is found who has seen the production. What is the expected number of residents the researcher will need to ask to find someone who has seen the production? a- 0.30 b- 0.09 c- 11.11 d- 11.00 e- 10.60

c 9/100 then divide both sides by nine to get 1/11.11 so about every 11.11 people will give you 1 person who has seen it

A local amusement park has 30 rides that park visitors can go on. The following table shows the relative frequency distribution for the number of rides that a park visitor will typically go on during one day at the park. The table also shows the deviation, or difference, from 21, the mean of the distribution. # of rides: 10 | 15 | 20 | 25 | 30 Deviation: -11 | -6 | -1 | 4 | 9 Relative frq: .1 | .2 | .2 | .4 | .1 Which of the following is closest to the standard deviation of the distribution? a- 7.07 b- 34 c- 5.83 d- 7.90 e- 20

c calculator

A local department store estimates that 10 percent of its customers return the merchandise they purchase. Let the random variable R represent the number of returns for a random sample of 40 customers. Assume that random variable R follows a binomial distribution. What is described by the value of (40 8)(0.1)^8(0.9)^32 ? A- The mean of the random variable B- The variance of the random variable C- The standard deviation of the random variable D- The probability that 8 customers in the sample will return merchandise E- The probability of selecting a sample of 40 customers who will all return merchandise

d

According to a 2015 Census Bureau survey, 75,511 of the 822,959 residents of Baltimore County, Maryland, were enrolled in college. Consider a sample of 800 residents of Baltimore County, Maryland in 2015 selected at random. Which of the following is closest to the expected value of the number in the sample enrolled in college? A- 8.17 B- 28.3 C- 66.7 D- 73.4 E- 94.4

d

In a certain region, 10 percent of the homes have solar panels. A city official is investigating energy consumption for homes within the region. Each week, the city official selects a random sample of homes from the region. Let random variable Y represent the number of homes selected at random from the region until a home that has solar panels is selected. The random variable Y has a geometric distribution with a mean of 10. Which of the following is the best interpretation of the mean? a- For a randomly selected week, it will take 10 homes before a home with solar panels is selected. b- Over many weeks, the average number of homes with solar panels is 10. c- Each week, the number of homes with solar panels increases by 10. d- Over many weeks, it takes 10 homes, on average, before a home with solar panels is selected. e- The average number of solar panels per home is equal to 10.

d

Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram support Alfonso's claim? a- Yes, the distribution is symmetric with a mean age of 36. b- No, the distribution is skewed to the left with a mean age of 36. c- No, the distribution is skewed to the right with a mean age greater than 36. d- No, the distribution is skewed to the left with a mean age greater than 36. e- No, the distribution is skewed to the right with a mean age of 36.

d

Parker has a part-time job picking apples. Let the random variable A represent the number of baskets of apples picked each day. The distribution of A has mean 4.5 baskets and standard deviation 1.3 baskets. Parker is paid $65 per day plus $5 per basket. What are the mean μ and standard deviation σ of Parker's daily pay? a- μ=$22.50 and σ=$6.50 b- μ=$87.50 and σ=$71.50 c- μ=$22.50 and σ=$71.50 d- μ=$87.50 and σ=$6.50 e- μ=$87.50 and σ=$1.30

d

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once? a- 0.72 b- 0.12 c- 0.1875 d- 0.15 e- 0.345

d .4*.375

While investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time. Additionally, 65 percent of the flights are overbooked, and 72 percent are late or not overbooked. One Sonic Air flight will be selected at random. What is the probability that the flight selected will be late and not overbooked? a- 0.21 b- 0.39 c- 0.26 d- 0.23 e- 0.72

d P(A∪B)[or] = P(A) + P(B) - P(A∩B)[and] (A∪B)= .72 P(A)= .6 P(B)=.35 P(A∩B)=? sooo .72=.6+.35-x x+.72=.95 x=.23

Given independent events A and B such that P(A)=0.3 and P(B)=0.5, which of the following is a correct statement? a- P(A∪B)=0.80 b- P(A|B)=0.5 c- P(B|A)=0.3 d- P(A∪B)=0.65 e- P(A|B)=0

d since they're independent, P(A∪B)[or] = P(A) + P(B) - P(A∩B)[and] so .8-.15=.65

A survey of people on pizza preferences indicated that 55 percent preferred pepperoni only, 30 percent preferred mushroom only, and 15 percent preferred something other than pepperoni and mushroom. Suppose one person who was surveyed will be selected at random. Let P represent the event that the selected person preferred pepperoni, and let M represent the event that the selected person preferred mushroom. Are P and M mutually exclusive events for the people in this survey? a- Yes, because the joint probability of P and M is greater than 0. b- Yes, because the joint probability of P and M is greater than 1. c- No, because the joint probability of P and M is equal to 1. d- Yes, because the joint probability of P and M is equal to 0. e- No, because the joint probability of P and M is equal to 0.

d they only asked for one topping so they couldn't have said both pepperoni and mushrooms

The distribution of weights of African bush elephants is skewed to the right with mean 6.42 tons and standard deviation 1.07 tons. Let the random variable W represent the weight, in tons, of a randomly selected elephant. The weight is converted to kilograms using the formula Y=900W. Which of the following best describes the distribution of Y ? a- Roughly symmetric with mean 5,778 kilograms and standard deviation 963 kilograms b- Roughly symmetric with mean 5,778 kilograms and standard deviation 1.07 kilograms c- Skewed to the right with mean 5,778 kilograms and standard deviation 1.07 kilograms d- Skewed to the right with mean 906.42 kilograms and standard deviation 1.07 kilograms e- Skewed to the right with mean 5,778 kilograms and standard deviation 963 kilograms

e

A hockey all-star game has the Eastern Division all-stars play against the Western Division all-stars. On the Eastern Division team there are 8 United States-born players, 14 Canadian-born players, and 2 European-born players. On the Western Division team there are 12 United States-born players, 8 Canadian-born players, and 4 European-born players. If one player is selected at random from the Eastern Division team and one player is selected at random from the Western Division team, what is the probability that neither player will be a Canadian-born player? a- 676/2304 b- 464/576 c- 4/9 d- 112/576 e- 160/576

e 10/24* 16/24 aka 10*16= 160 24*24=576

Let the random variable X represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of X. amount. -1 | 1 | 10 probability .8 | .15 | .05 Which of the following statements is the best interpretation of the mean of X ? In the long run, the player will (gain/lose) an average of $_____ per carnival game played.

lose, $0.15