AP Statistics Random Variable

If r = 1 , the standard deviation of y is equal to the standard deviation of the residuals.

• True

• False

A random variable is continuous if the set of possible values includes an entire interval on the number line.

• True

• False

For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b.

• True

• False

Answer explanation

Area under the curve is the probability not the height

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The expected value of X is E(X) =

• 0.40

• 1.00

• 1.45

• 1.66

• 2.50

• A

• B

• C

• D

• E

The time it takes for a light bulb to burn out. 

• Discrete random variable

• Continuous random variable

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Is this a probability distribution?

• No

• Yes

Identify the type of random variable: number of books in a library

• Discrete Random Variable

• Continuous Random Variable

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The standard deviation of X is 1.27. Interpret this value.

• The number of computers in a randomly selected household is within 1.27 of the mean.

• The number of computers in a randomly selected household is exactly 1.27 from the mean.

• The number of computers in a randomly selected household is 1.27, on average.

• The number of computers in a randomly selected household is typically 1.27 from the mean.

• The average number of computers in a randomly selected household is typically 1.27 from the mean.