Unit Test 10

Draw a histogram for the intervals 16-18, 19-21, 22-24, and 25-27 using the following data: 26, 16, 22, 27, 20, 24, 21, 27, 22, 21, 26, 27, 23, 20, 16, 17, 27, 19, 17, 17

A.

Consider a game in which you draw playing cards from a standard 52-card deck, one at a time. If a player draws a face card (a jack, a queen, or a king), the player is awarded 10 points. Any other card drawn costs the player 3 points. What is the expected value of drawing a card in this game?

A. 0 points

A game show has a bonus round where a contestant gets to spin a balanced wheel that is divided into eighths. The contestants win cans of turtle wax based on which number they land on. How many cans of turtle wax can the game show expect to give out per player in the long run? Round the answer to the nearest whole number.

A. 142

Ralphie is taking a ten-question multiple choice test. Each question has five choices. If Ralphie answers a question correctly, he earns one point; if he answers incorrectly, he loses half a point. Ralphie answers the first six questions correctly, then guesses on the last four. What is the expected value of his test score? Round the answer to the nearest whole percent.

A. 52%

A charity is selling raffle tickets at $5 apiece. Out of the 100 tickets sold, ten third-place winners will be drawn, each winning $20. Five second-place winners will be drawn, each winning $50. Lastly, one grand prize of $100 will be awarded. Is a raffle with these rules a good idea for the charity? Why or why not?

A. No, because one ticket's expected value is worth $0.50 more than the face value.

You are a contestant on a game show called "Bargain or No Bargain." You are presented with three briefcases, which contain rewards of $700,000, $1,000, and $100. The host of the show says you can either open one random case and keep the amount inside, or you can accept a guaranteed award of $240,000. What is the mathematically correct decision, and why?

A. Take the $240,000, because it is greater than the expected value of the briefcases.

Greg flips a coin, then rolls a standard number cube. Construct the sample space showng all the possible outcomes of Greg's experiments.

B (the long one lmao)

A coin is selected at random from a bag of money. Use the distribution table above to determine the expected value. Round the answer to the nearest cent.

B. $0.11

In a certain board game, a number cube is rolled to determine the number of spaces a player gets to move. Use the table above to determine the expected value of the number of spaces a player moves. Round the answer to the nearest tenth.

B. 1.3

A dart is thrown at a dartboard and hits it in a random location. The probability of each point value possible is given in the table above. What is the expected value of the dart? Round the answer to the nearest tenth.

B. 7.2

You are a contestant on a game show called "Bargain or No Bargain." You are presented with three briefcases, which contain rewards of $500,000, $2,000, and $500. The host of the show says you can either open one random case and keep the amount inside, or you can accept a guaranteed award of $160,000. What is the mathematically correct decision, and why?

B. Choose a briefcase, because the expected value is greater than $160,000.

Malik is considering investing $900 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 150%, and a 50% chance that he will lose his initial investment. Determine if Malik should make the investment, and find the expected value of the investment.

B. No, the expected value is -$45.

A coin is selected at random from a bag of money. Use the distribution table above to determine the expected value. Round the answer to the nearest cent.

C. $0.10

Use the probability model above to determine the expected value of the return of the investment.

C. $90

Consider a game in which you flip a coin. If it comes up heads, you earn 1 point; if it comes up tails, you earn 0 points. What is the expected value of one coin flip?

C. 0.5

Which of the following statements about the expected value of a random experiment is true?

C. As the number of trials gets larger, the average of the trials approaches the expected value.

Which of the following events has an expected value that is in the sample space?

C. randomly picking a number between one and nine, inclusive

Draw a histogram for the intervals 17-19, 20-22, 23-25, and 26-28 using the following data: 19, 19, 27, 20, 27, 26, 25, 26, 18, 27, 20, 24, 19, 21, 27, 23, 21, 17, 22, 22

D.

Use the probability model above to determine the successful outcome's contribution to the expected value of the return.

D. $630

Consider a game in which you flip a coin. If it comes up heads, you earn 2 points; if it comes up tails, you earn 4 points. What is the expected value of one coin flip?

D. 3

A normal distribution is bell-shaped and symmetric about its mean.

True

In a certain normal distribution of scores, the mean is 40 and the standard deviation is 3. Find the z-score corresponding to a score of 54.

a. 4.67

A set of data is normally distributed with a mean of 455 and a standard deviation of 25. What percent of the data is in the interval 405-455?

a. 47.5%

Is the data set "the hair color of the presidents of the United States" quantitative or qualitative? If it is quantitative, is it discrete or continuous?

a. qualitative

Is the data set "heights of the women in the U.S. Congress" quantitative or qualitative? If it is quantitative, is it discrete or continuous?

a. quantitative, continuous

Is the data set "the number of leaves on a branch" quantitative or qualitative? If it is quantitative, is it discrete or continuous?

a. quantitative, discrete

A set of data is normally distributed with a mean of 75 and a standard deviation of 3. What percent of the data is in the interval 72-78?

b. 68.3%

A student took two national standardized tests while applying for college. On the first test, = 475 and = 75, and on the second test = 32 and = 6. If he scored 630 on the first test and 45 on the second test, on which test did he do better?

b. second test

Given the data, as shown in the image below, determine if the distribution is uniformly distributed, symmetrically distributed, skewed right, or skewed left.

b. skewed left

A sample of restaurants in a city showed that the average cost of a glass of iced tea is $1.25 with a standard deviation of 7¢. If a new restaurant charges a price for iced tea that has a z-value of -1.25, then what is the tea's actual cost?

c. $1.16

In a certain normal distribution of scores, the mean is 50 and the standard deviation is 6. Find the z-score corresponding to a score of 60.

c. 1.67

The heights of a certain group of adult males was found to be normally distributed. The mean height is 170 cm with a standard deviation of 6 cm. In a group of 1200 of these males, about how many would be more than 164 cm tall?

c. 1010

A set of data is normally distributed with a mean of 86 and a standard deviation of 1.5. What percent of the data is in the interval 86-87.5?

c. 34.15%

The average daily temperatures of a city in theUnited States were recorded for one year. The graph below shows the information. What is the median and the standard deviation of the average daily temperatures of this city?

c. 84; 6

The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs. Identify the population and the sample.

c. population: 10 shipments of 1000 cartons of eggs sample: every 50th carton in each shipment

Is the data set "distance a baseball travels after being hit" quantitative or qualitative? If it is quantitative, is it discrete or continuous?

c. quantitative, continuous

Is the data set calories burned while running a marathon quantitative or qualitative? If it is quantitative, is it discrete or continuous?

c. quantitative, continuous

Given the data, as shown in the image below, determine if the distribution is uniformly distributed, symmetrically distributed, skewed right, or skewed left.

c. uniform

In a certain normal distribution of scores, the mean is 30 and the standard deviation is 3. Find the z-score corresponding to a score of 23.

d. -2.33

Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º. Estimate the probability that the temperature on a given day in February is 22º or lower.

d. 0.16

Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º. Estimate the probability that the temperature on a given day in February is 39º or higher.

d. 0.16

The heights of 1000 students at a local school were recorded and found to be approximated by the normal curve below. Which answer could represent the mean and standard deviation for these data?

d. 66, 4

Given the data, as shown in the image below, determine if the distribution is uniformly distributed, symmetrically distributed, skewed right, or skewed left.

d. skewed right