# HiSET Mathematics: Probability Distributions Chapter Exam

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#### Question 1 1. Which of the following is NOT a property of a random variable?

#### Question 2 2. A television channel conducts a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. How many TVs does each household have on average?

#### Question 3 3. An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x?

#### Question 4 4. The tail lengths of a certain animal are normally distributed with a mean length of 1.5 feet and a standard deviation of 3 inches. What percentage of these animals have a tail that is at most one foot long?

#### Question 5 5. From mortality tables it has been determined that the probability of a 20-year old male non-smoker dying within the year is 0.0035. Suppose an insurance company wants to sell a $50,000 1-year life insurance policy to a 20-year old non-smoking male. What should they charge for the policy to break even?

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#### Question 6 6. You decide to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values?

#### Question 7 7. Suppose you toss a coin twice, what is the probability you get two heads in row?

#### Question 8 8. From mortality tables it has been determined that the probability of a 20-year old female non-smoker dying within the year is 0.0023. Suppose an insurance company wants to sell a $60,000 1-year term life insurance policy to a 20-year old non-smoking female. What should they charge for the policy to make a profit of $30 per policy?

#### Question 9 9. You decide to collect a bunch of cans of soda and measure the volume of soda in each can. Let x = the number of mL of soda in each can. What type of variable is x?

#### Question 10 10. You are creating a tree house and have made the doorway into the structure 71 inches tall. Suppose the average height of adult males is 68 inches with a standard deviation of 3 inches. What percentage of men will have to bend their heads to get into the house?

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#### Question 11 11. Suppose you toss three coins. What is the probability that you get two heads and one tail if the order in which you get them does not matter?

#### Question 12 12. The lifespan of a certain battery is measured in cycles. A manufacturer claims that the average number of cycles for their battery is 2000 with a standard deviation of 100, and the number of cycles is distributed normally. You wish to buy a battery from this manufacturer. What is the probability that the battery will last between 1900 and 2200 cycles?

#### Question 13 13. A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). Suppose that for a bet of $1 on red, the casino will pay you $2 if the ball lands on a red slot (a net gain of $1), and otherwise you lose your dollar. What can you expect to win or lose in this game?

#### Question 14 14. A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). On one spin of the roulette wheel, what is the probability that the ball lands on a red slot?

#### Question 15 15. Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. Let X = the number of firearms in a household. From the survey of 30,000 households it was determined that the empirical probability of X = 1 was 0.2. How many of the households in the survey had one firearm in their home?

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#### Question 16 16. Which of the following is NOT a property of the Normal Distribution?

#### Question 17 17. Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. If the sample size was 25,000 and 17,000 households reported that they had no firearms in their home, what would be the empirical probability that a randomly selected household had no firearms in their home?

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Question 18
18.
Consider the following probability distribution (see table below) of the number of firearms in a household, constructed from a survey of 25,000 randomly selected households. Let X = the number of firearms in a household, and assume that the probability of a household having more than 6 firearms in the home is negligible. If a household is selected at random, then how many firearms would you *expect* them to have?

#### Question 19 19. Suppose you toss three coins, what is the probability you get three heads?

#### Question 20 20. In a certain video game you wish to be in the top 0.15% of the scores. Assuming that the scores are normally distributed with a mean score of 25,460 and a standard deviation of 570, what is the score you need to achieve?

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#### Question 21 21. Suppose you play a game where you spin a spinner (see picture below) with areas of the colors on the spinner broken down as shown: 10% blue, 60% green, and 30% red. In addition, if the spinner lands on red you win 6 points, if it lands on blue you win 1 point, and if it lands on green you lose 5 points. If you keep spinning, how many points can you expect to win or lose per game?

#### Question 22 22. You play a game where you toss a coin. On each toss if it lands with heads up, you win $1. However, if it lands with tails up, you lose $2. If you continue to play this game, how much can you expect to win or lose per game?

#### Question 23 23. A distribution of data has a mean of 15 and a standard deviation of 2. How many standard deviations away from the mean is a value of 13?

#### Question 24 24. You conduct an experiment where you want to measure the number of rolls it takes to get two 6's in a row when you roll a fair six-sided die. State whether the random variable is discrete or continuous and give a summary of its values.

#### HiSET Mathematics: Probability Distributions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!