AP Statistics Chapter 6 Review

Consider the following set of random variables: I. Total number of points scored during a football game II. Lifespan in hours of a halogen light bulb III. Height in feet of the ocean's tide at a given location IV. Number of fatalities in civilian aircraft crashes in a given year V. Length in inches of an adult rattlesnake. Which ones are continuous random variables?

In a particular game, a ball is randomly chosen from a box that contains three red balls, one green ball, and six blue balls. If a red ball is selected, you win $2. If a green ball is selected, you win $4. If a blue ball is selected, you win nothing. Let X be the amount that you win. The expected value of X is

The time in minutes X that you must wait before a train arrives at your local subway station is a uniformly distributed random variable between 5 minutes and 15 minutes. That is, the density curve of the distribution of x has constant height between 5 and 15 and height 0 outside this interval. Determine P (6 < X < 8).

The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to

A widget manufacturer estimates that the total weekly cost in dollars, C, to produce x widgets is given by the linear function C(x) = 500 + 10x, where the intercept 500 represents a "fixed" cost of manufacture and the slope 10 represents the "variable" cost of producing a certain number of widgets. Analysis of weekly widget production reveals that the number of widgets X produced in a week is a random variable with mean μX = 200 and standard deviation σX = 20. What are the mean and the standard deviation of C?

Suppose that we are given random variables X, Y for which we know the means μ X, μ Y and the variances σ2X, σ2Y. Which of the following quantities could we not compute without knowing some additional information about X, Y?

The daily total sales (except for Saturday) at a small restaurant have a probability distribution that is approximately Normal with a mean of μ = $530 and a standard deviation of σ = $120. The probability the sales will exceed $700 on a given day is approximately

A set of 10 playing cards consists of five red cards and five black cards. The cards are shuffled thoroughly, and we draw four cards one at a time and without replacement. Let X = the number of red cards drawn. The random variable X has which of the following probability distributions?

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. If the student needs at least 40 points to pass the exam, the probability that she passes is closest to

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The probability that the student scores lower than a 60 on the exam is

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is

For which of the following choices of n, p can we not use the Normal approximation to the binomial distribution?

In the gambling game of chuck-a-luck, three dice are rolled using a rotating, hourglass-shaped cage. The player chooses one of the six possible sides (1, 2, 3, 4, 5, or 6) and receives a payoff the amount of which depends on how many dice turn up on that particular side. Let X = the number of times the dice have to be rolled until we see "three of a kind" (of any type). Which of the following probability distributions does X have?