algebra II last test, Unit Test Unit Test Review algebra II, Hypothesis Testing, Applications with Standard Normal Distribution, Binomial Distribution, Expected Value, Properties of Probability Distributions

When j = 32, m = 2, and p = mc004-1.jpg. If j varies directly with m and inversely with p, what is the constant of variation?

4

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

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 city's mean annual rainfall?

40.5 inches

A company plans to sell embroidered hats for $15 each. The company's financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?

401

The ideal gas law states that the volume, v, of a gas in liters varies directly with the amount of the gas in moles, n, and the absolute temperature in Kelvin, T, and varies inversely with the pressure, P, of the gas. Two moles of a gas has a volume of 35.424 L at 270 Kelvin when P = 1.25 atm. What is the volume of 3 moles of a gas at 280 Kelvin when P = 1.5 atm?

45.92 L

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 rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350. Which most restrictive level of significance would suggest that the company should raise rates

5%

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 0.7995 1.00 0.8413

66%

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 at least one day per week?

83%

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

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

$2.50

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?

$2600

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.

$3.70

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 the customer when repairing the item, how much should the company charge to make a profit of $2.00 per item?

$8.00

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 groups of teachers had different levels of job satisfaction. They will use a significance level of 5% for their test.

-1.96 and 1.96

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?

-1/6

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

-5.30

A gymnastics coach records the scores of a gymnast and develops the probability distribution below. What is the probability the gymnast scores a 9 or 9.5?

0.14

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

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

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

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that at most 4 students have taken chemistry? Round the answer to the nearest thousandth.

0.438

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

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

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 a home run and 5 points for each home run?

0.57

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. mc020-1.jpg z Probability 0.00 0.5000 1.00 0.8413 2.00 0.9772 3.00 0.9987

0.86

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

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. Which of the following is the probability distribution, PX(x)?

1

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 following is the correct probability distribution?

1

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 of pets as the random variable, X, which of the following is the probability distribution, PX(x)?

1

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 2.5 hours. Which of the following is the most restrictive level that would validate his claim?

1%

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

1.08 seconds

Vladimir rolls a six-sided number cube 36 times. If getting a 3 is a success, what is the probability of a success?

1/6

A scientist calculated the mean and standard deviation of a data set to be mc026-1.jpg and mc026-2.jpg. She then found that she was missing one data value from the set. She knows that the missing data value was exactly 3 standard deviations away from the mean. What was the missing data value?

147

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? Use the portion of the standard normal table below to help answer the question.

16%

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 vote between 0.37 and 0.39? Use the portion of the standard normal table below to help answer the question.

17%

How many outcomes are possible for one event of a binomial experiment?

2

Which of the following represents a valid probability distribution?

2

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 standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298.4 mL. Which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL?

2.5%

The quantity n varies jointly with the product of z and the square of the sum of x and y. When n is 18, x = 2, y = 1, and z = 3. What is the constant of variation?

2/3

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

The potential energy of an object is jointly related with the mass of the object and the height of the object. A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules. A 10-kg object is 3 meters off the ground. What is the potential energy of the 10-kg object

294 joules

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

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 months and 3 years 3 months? Use the portion of the standard normal table below to help answer the question.

32%

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?

90.8

About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?

95%

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.

Which of the following is a binomial experiment?

A survey asking 75 people if they like the new school building

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 included as hits in the table.

E(Jeter) = 0.38 and E(Pujols) = 0.45, so back Pujols.

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 includes the point scheme.

E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.

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.

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 data on 10 random students and finds that the average time to take the quiz was only 25 minutes. As a result, the teacher performs a two-tailed hypothesis test with a significance level of 5%. Which conclusion is valid based on the results of the test?

Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.

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.

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

It is a favorable game.

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.

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

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 for the last 40 receipts. She needs to know if this falls below the chain's average. She will use a 1% level for significance because she does not want to inadvertently report the restaurants income as below average.

She should reject H0 : µ = 72 and accept Ha : µ < 72.

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

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.

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 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, teachers give a score of 3.3 out of 5 with a standard deviation of 0.6. When the authors of the study interviewed 40 teachers who supplemented with their own materials, they found 3.5 to be the mean. The authors wanted to know if the group of teachers that could choose supplementary curriculum had a higher level of job satisfaction. They used a significance level of 1%. Which of the following statements is valid based on the results of the test

The data shows that the authors cannot make a determination either way with this data.

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 times. Which statement must be true?

The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing

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 standard deviations from the mean?

The probability is equal to p%.

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 random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?

The z-statistic is 3.32, so the null hypothesis should be rejected.

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.

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 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 correctly models the expected value of this investment?

a

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 from 20 people in her high school and found that the average price spent on a prom dress was $208.00. Which of the following are the correct null hypothesis and alternate hypothesis?

a

For a standard normal distribution, which of the following variables always equals 0?

a

Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

a

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 expected value for a ticket?

b

For a standard normal distribution, which of the following variables always equals 1?

b

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

A store owner buys $4,000 worth of products. For shipping costs, it is 10% of the amount of product A and 4% of the amount of product B. If the total shipping cost is $352, which system of equations can be used to determine how much of product A and product B the store owner bought?

c

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 from the average. Which of the following are the correct null hypothesis and alternate hypothesis?

c

Which of the following statements is equivalent to mc015-1.jpg?

c

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 distribution?

positively skewed

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

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 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.