AP STATS Unit 3

Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than

$255

It has been estimated that as many as 70% of the fish caught in certain areas of the Great Lakes have liver cancer due to the pollutants present. A sample of 130 fish is caught and inspected for signs of liver cancer. The number of infected fish within two standard deviations of the mean is

(81, 101)

A survey asks a random sample of 1200 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let p hat denote the proportion in the sample who say they support the increase. Suppose that 30% of all adults in Ohio support the increase. The standard deviation of p hat is

0.0132

The probability that you win on one or more of your 3 plays of the game in the previous question is about

0.06

The Gallup Poll has decided to increase the size of its random sample of Canadian voters from about 1500 to about 4000 people right before an election. The poll is designed to estimate the proportion of Canadian voters who favor a new law banning smoking in public buildings. The effect of this increase is to

reduce the variability of the estimate

If a population has a standard deviation σ, then the standard deviation of the mean of 100 randomly selected items from this population is

σ/10

An instant lottery game gives you probability of 0.02 of winning on any one play. Plays are independent of each other. If you play 3 times, the probability that you win on none of your plays is about

0.94

A cell phone manufacturer claims that 92% of the cell phones of a certain model are free of defects. Assuming that this claim is accurate, how many cell phones would you expect to have to test until you find a defective phone?

12.5

A factory makes silicon chips for use in computers. It is known that about 85% of the chips meet specifications. Every hour a sample of 15 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 15 chips and determine the number meeting specifications in each sample. What is the mean of the number of chips meeting specifications?

12.75

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05 ounces with a standard deviation of 0.1 ounce. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the observations should occur in which interval?

15.95 - 16.15 ounces

Use the following information for questions 11 - 13. A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution: X 1 2 3 4 P(X) 0.2 0.4 0.3 0.1 The mean μof X is

2.3

A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5,000 with probability 9/20, to break even with probability 5/20, and to lose $5,000 with probability 3/20. The expected profit in dollars is

3000

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?

72% is a statistic and 56% is a parameter

A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let X be the number of cards you turn over until you observe the first red card. The random variable X has which of the following probability distributions?

None of these

Use the following information for questions 1 - 4. Government data give the following counts of violent deaths in a recent year among people 20 to 24 years of age by sex and cause of death: Female Male Accidents 1818 6457 Homicide 457 2870 Suicide 345 2152 Let A be the event that a victim of violent death was a woman and B the event that the death was a suicide. The proportion of suicides among violent deaths of women is expressed in probability notation as

P(B|A)

Which of the following random variables should be considered continuous?

The time it takes for a randomly chosen woman to run 100 meters.

A random variable is

a variable whose value is a numerical outcome of a random phenomenon

A random sample of 15 people is taken from a population in which 40% favor a particular political stand. What is the probability that exactly 6 individuals in the sample favor this political stand?

0.2066

Use the following information for questions 11 - 13. A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution: X 1 2 3 4 P(X) 0.2 0.4 0.3 0.1 Using the above data, what is the probability that a randomly chosen subject completes at least 3 puzzles in a five-minute period while listening to soothing music?

0.4

Use the following information for questions 1 - 4. Government data give the following counts of violent deaths in a recent year among people 20 to 24 years of age by sex and cause of death: Female Male Accidents 1818 6457 Homicide 457 2870 Suicide 345 2152 The conditional probability that the death was accidental, given that the victim was male, is about

0.56

Use the following information for questions 11 - 13. A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution: X 1 2 3 4 P(X) 0.2 0.4 0.3 0.1 Find P(X < 3)

0.6

In a certain large population, 40% of households have a total annual income of at least $70,000. A SRS of 5 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of at least $70,000?

0.66304

Use the following information for questions 1 - 4. Government data give the following counts of violent deaths in a recent year among people 20 to 24 years of age by sex and cause of death: Female Male Accidents 1818 6457 Homicide 457 2870 Suicide 345 2152 The conditional probability that the victim was male, given that the death was accidental, is about

0.78

Use the following information for questions 1 - 4. Government data give the following counts of violent deaths in a recent year among people 20 to 24 years of age by sex and cause of death: Female Male Accidents 1818 6457 Homicide 457 2870 Suicide 345 2152 Choose a violent death in this age group at random. The probability that the victim was male it about

0.81