AP Statistics Chapter 6 Random Variables

(6.1) A probability model ________________________.

• describes the possible outcomes of a chance process and the likelihood that those outcomes will occur.

• is a numerical variable that describes the outcomes of a chance process.

(6.1) The probabilities in probability distributions must meet what requirement(s)?

• Each probability is between 0 and 1 & The sum of all the probabilities is 1

• The sum of all the probabilities is 1

• All probabilities are the same (ex: .3, .3, .3)

• Each probability is between 0 & 1 and all probabilities are the same (ex: .3, .3, .3)

(6.2) How does multiplying or dividing by a constant affect a random variable? (Select all correct answers)

• Multiplies (divides) measures of center and location (mean, median, quartiles, percentiles) by b.

• Does not change measures of center and location (mean, median, quartiles, percentiles) by b.

• Multiplies (divides) measures of spread (range, IQR, standard deviation) by |b|.

• Does not change measures of spread (range, IQR, standard deviation) by |b|.

(6.3) The four conditions for a binomial setting are:

• Binary, Independent, Normal, Success

• Binary, Independent, Number, Success

• Binary, Trials, Number, Success

• Binary, Independent, Trials, Success

(6.1) What is the expected value of this probability distribution?

• 10

• 1.99

• 1.092

• 1

(6.2) How does adding or subtracting a constant affect a random variable?

• Adds/subtracts ‘a’ to measures of center and location (mean, median, quartiles, percentiles).

• Does not change measures of center and location (mean, median, quartiles, percentiles).

• Adds/subtracts ‘a’ to measures of spread (range, IQR, standard deviation).

• Does not change measures of spread (range, IQR, standard deviation).

(6.3) What is the difference in the conditions for binomial and geometric settings?

• There is no difference between them

• In binomial settings, the number of trials are fixed in advanced. In geometric settings, the number of trials are not set in advance.

• In binomial settings, trials must in independent. In geometric settings, trials do not have to be independent.

• In geometric settings, the number of trials are fixed in advanced. In binomial settings, the number of trials are not set in advance.

(6.1) Formula and definition of the standard deviation of a random variable

• (x value - mean)^2 (probability) - the average amount a randomly selected value will differ from the mean

• (x value) (probability) - the average amount a randomly selected value will differ from the mean

• (x value - mean)^2 (probability) - the average amount a randomly selected value will differ from the median

• (x value) (probability) - an average of all possible outcomes

(6.2) Let X = the number of passengers on a randomly selected trip with Pete’s Jeep Tours. Y = the number of passengers on a randomly selected trip with Erin’s Adventures. Define T = X + Y. How many total passengers can Pete and Erin expect on a randomly selected day?

• 6.85

• 4.84

• 2.033

• 4.043

(6.3) The mean (expected value) of a geometric random variable Y is _______.

• 1/p

• P(Y = k) = (1 - p)^( k1) p

• n(1 - p) ≥ 10

• np