Standard Deviation and Expected Value of Random Variables

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately Normal with mean $360 and standard deviation $50. The least profitable 10% of days have a profit of at most how many dollars?

• $244

• $296

• $370

• $424

• $476

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 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.

A marketing survey compiled data on the number of personal computers in households. X = the number of computers in a randomly-selected household. If you were to randomly select households, what is the probability it would take exactly 8 selections to find one with 5 computers?

• Approximately 0

• 0.02

• 0.03

• 0.32

• Approximately 1

The graph shows the probability distribution for the number of orders per week for a randomly selected week at an Etsy store. What is the expected number of orders and the standard deviations of the number of orders?

• 44.5, 2.449

• 44.5, 2.291

• 44.64, 1.694

• 44.64, 1.672

• A

• B

• C

• D

• E

The model shown above shows the probability for rental units based on the number of rooms. What is the expected value and the standard deviation of the number of rooms in a rental unit?

• 5, 2.7386

• 5, 2.5820

• 4.355, 1.5647

• 4.355, 1.2996

• A

• B

• C

• D

• E

• B
• C
• D
• E

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14

• 4.67

• 5

• 7.5