AP Stats Random Variables

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20
• 0.29
• 0.39
• 0.61

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the expected value of the number of cars in a randomly selected household? 

• 2.5
• 0.1667
• 1.45
• 1

Choose the best answer.

• B
• C
• D
• E

Random variable X is normally distributed with mean 10 and standard deviation 3, and random variable Y is normally distributed with mean 9 and standard deviation 4. If X and Y are independent, which of the following describes the distribution of Y - X?

• Normal with mean 1 and standard deviation -1
• Normal with mean -1 and standard deviation -1
• Normal with mean -1 and standard deviation 5
• Normal with mean -1 and standard deviation 7

Two blue cubes and three green cubes, each with faces labeled 1-6, will be rolled.  Letting X be the total score for the two blue cubes and Y be the total score for the three green cubes, it can be shown that the standard deviations of the random variables X and Y are 2.42 and 2.96, respectively.  Which of the following is the standard deviation of X - Y?

• -2.91
• -0.54
• 3.82
• 14.62

Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation of 47, and that for detective novels the number of pages has mean 404 and standard deviation 173.  A reader is going to select at random one romance novel, independently selected at random one detective novel and read both book.  What is the expected number of total pages the person will read? 

• 988
• 768
• 543.8
• 40

Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation of 47, and that for detective novels the number of pages has mean 404 and standard deviation 173.  A reader is going to select at random one romance novel, independently selected at random one detective novel and read both book. What is the standard deviation of the total number of pages the person will read? 

• 14.8
• 110.0
• 179.3
• 220.0

In a large country, the distribution of the heights of married men is normal with mean 68.9 inches and standard deviation 2.9 inches.  The distribution of the heights of married women is normal with mean 63.8 and standard deviation 2.5 inches. 
A married couple is to be chosen at random.  Let the random variable Z be the sum of the height of the man and the height of the woman. 
Which of the following statements can be concluded from the information given?
I.  Mean of Z = 68.9 + 63.8
II.  Standard Deviation of Z = sqrt(2.9² + 2.5²)
III.  The distribution of Z is normal.

• I only
• III only
• I and II only
• I, II and III

Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day.  The expected value of X is $0.47 and the standard deviation of X is $0.15.  
If a customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?

• $3.00
• $0.47
• $0.67
• $9.40

Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?

• 0.91
• 0.09
• 0.14
• 0.86