A supervisor finds the mean number of miles that the employees in a department live from work. He finds mc022-1.jpg and mc022-2.jpg. Which statement must be true?
z37 is between 2 and 3 standard deviations of the mean.
Kavita has been assigned the task of studying the average customer receipt for a branch of a major restaurant chain. The average receipt for the chain is $72.00 with a standard deviation of $11.00. The branch she is studying has an average bill of $67.00
She should reject H0 : � = 72 and accept Ha : � < 72.
The life spans of a computer manufacturer's hard drives are normally distributed, with a mean of 3 years 6 months and a standard deviation of 9 months. What is the probability of a randomly selected hard drive from the company lasting between 2 years 3 mo
32%
Derek Jeter challenges Albert Pujols to a batting battle. Each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. Which player should you back given the statistics in the table below? Note that home runs are inclu
E(Jeter) = 0.38 and E(Pujols) = 0.45, so back Pujols.
The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day?
0.92
Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?
Removing the outlier will decrease the spread of the graph of the data set.
Miguel Cabrera has had 369 at bats, and he has 127 hits and 21 home runs. (Note: The home runs are included in the hits data.) If he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not
0.57
Weston completed a hypothesis test and found that he could not reject the null hypothesis. Which of the following is a valid reason for his conclusion?
The z-statistic lies outside the critical region.
A textbook company states that the average time a student needs to take a quiz from its book is 30 minutes with a standard deviation of 3 minutes. A teacher using the book is not sure that this is correct for her classes and wants to check. She collects d
Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.
A city's annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by mc017-1.jpg. If the standard deviation of the city's yearly rainfall totals is 1.8 inches, what is the cit
40.5 inches
Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with ra
5%
A company makes a product and has no way to determine which ones are faulty until an unhappy customer returns it. Three percent of the products are faulty and will cost the company $200 each in customer service and repairs. If the company does not refund
$8.00
The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. What is the probability that a sample chosen at random has a proportion of registered voters who
17%
A company has an opportunity to bid on three contracts. Determine which would be the best investment given the information in the table below.
Southeast
A local newspaper compiles data on the number of days, X, people in a neighborhood receive the newspaper. The probability distribution for the data is shown in the table below. What is the probability that a randomly chosen person receives the newspaper a
83%
Brett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20. His sample data has a mean of 295 and a sample size of 50. Which of the following correctly depicts the z-statistic for Brett's data
-5.3
The College Board states that the average math SAT score is 514 with a standard deviation of 117. Colleen gathered data from 50 students in her graduating class and found the average score to be 523. She thinks that her class's math SAT score is different
c
A recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a standard deviation of $12.00. Alyssa thinks that her school is more fashion conscious and that students spent more than $195.00. She collected data
a
A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. On average, when surveyed regarding job satisfaction, t
The data shows that the authors cannot make a determination either way with this data.
A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a ra
The z-statistic is 3.32, so the null hypothesis should be rejected.
A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. The authors of the study wanted to know if the two grou
-1.96 and 1.96
Tyesha found that the z-statistic was 2.1 and that the critical z-values were -1.96 and 1.96. Which of the following is a valid conclusion based on these results?
One can reject the null hypothesis.
1 6
A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a sta
2.50%
David wants to complete a hypothesis test with the least amount of probability for error. If he sets the significance level to 1%, assuming his sample is truly random, what else could he adjust in the test in order to reduce error?
He could increase the sample size.
Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting the null hypothesis?
The z-statistic lies in the critical region.
A popular video game claims that the average time needed to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours. James thinks that he and his four friends are more skilled than the average gamer because it took them an average of only
1%
For a standard normal distribution, find the approximate value of mc005-1.jpg. Use the portion of the standard normal table below to help answer the question.
z
Probability
0.00
0.5000
0.22
0.5871
0.32
0.6255
0.42
0.6628
0.44
0.6700
0.64
0.7389
0.84
0.799
66%
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
mc020-1.jpg
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.86
About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?
95%
Which of the following statements is equivalent to mc015-1.jpg?
c
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question.
mc009-1.jpg
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.81
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
mc016-1.jpg
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.18
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes?
16%
For a standard normal distribution, which of the following variables always equals 1?
b
The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to -z stan
The probability is equal to p%.
For a standard normal distribution, which of the following variables always equals 0?
a
How many outcomes are possible for one event of a binomial experiment?
2
A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?
250
Which of the following is a binomial experiment?
Flipping a coin 10 times and recording if it comes up heads
Franco has a hat with 9 blue marbles, 4 yellow marbles, and 12 green marbles. He designs a binomial experiment by drawing a marble from the hat, recording whether the marble is green, and then laying the marble aside. He then repeats the process seven tim
The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing
Two percent of mobile phones produced at a factory are defective. Which of the following is a binomial experiment?
Selecting 200 phones randomly and recording whether each phone is defective
Which of the following is a binomial experiment?
A survey asking 75 people if they like the new school building
Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth.
0.213
Janie flips a coin 70 times and records if it comes up heads. If getting heads is a success, what is the probability of a failure?
0.5
Dion flips a coin 20 times and records if it comes up heads. If getting heads is a success, what is the probability of a success on each roll?
0.5
According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth.
0.309
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
$2,600
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?
-0.166666667
A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expe
b
Sebastian has researched the following scoring schemes: one that has 5 question choices, one that has 4 question choices, and two that have 3 question choices. Which scoring scheme is the most favorable to the test taker?
scheme D
If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?
b
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 ans
90.8
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
$3.70
A business has an opportunity to invest $35,000. If the investment is a success, the business earns a profit of $150,000. Otherwise, the investment will result in a total loss of all monies. If the investment has 0.27 chance of success, which equation cor
a
Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?
It is a favorable game.
Which statement below correctly depicts the expected value of a fair game?
E(X) = 0
Two students devised a game called "3 Pennies & 2 Nickels." Each player will choose to play the pennies or the nickels. In each round, the players will flip all their coins on the table and record how many heads and tails they have. The table below includ
E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.
Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?
A number less than or equal to 3 will add one point.
A 4 will lose two points.
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 $2.90 on average for one gallon of milk.
A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. If the random variable is "yellow (Y)," which of the fol
1
Which of the following describes the probability distribution below?
mc007-1.jpg
The mean is greater than the median, and the majority of the data points are to the left of the mean.
Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. Eight of the students in the grade own 1 pet. Considering the number o
1
A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs.
1
Which of the following represents a valid probability distribution?
2
Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?
symmetric
A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of 50 spins. She computes and graphs the relative frequencies for each number. Which of the following describes the probability distributi
positively skewed
The number of siblings each student at a softball game has is recorded. The graph below shows the probability distribution of having any number of siblings, X, for a randomly selected student. Which number of siblings is least likely?
4 siblings
The graph below shows the experimental probability of a runner finishing in first place (1), in second place (2), in third place (3), or not placing (4). Which of the following describes the probability distribution?
negatively skewed
A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability distribution below?
3