Random Variables

Which of the following random variables should be considered continuous?

• The number of brothers a randomly chosen person has
• The number of orders received by a mail order company in a randomly chosen week
• The number of cars owned by a randomly chosen adult male
• The time it takes a randomly chosen woman to run 100 meters

The weight of reports produced in a certain department has a Normal distribution with mean 60g and standard deviation 12g.  What is the probability that the next report will weigh less than 45g?

• 0.1042
• 0.1056
• 0.3944
• 0.0418

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4 and if the number of spots showing is 1, 2 or 3, you win nothing. Let X be the amount you win.  What is the expected value of X?

• $
• $1
• $2.50
• $4

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4 and if the number of spots showing is 1, 2 or 3, you win nothing. Let X be the amount you win. What is the standard deviation of X?

• $1
• $1.35
• $1.41
• $1.78

The mp3 music files on Sharon’s computer have a mean size of 4.0 megabytes and a standard deviation of 1.8 megabytes. She wants to create a mix of 10 of the songs for a friend. Let the random variable T = the total size (in megabytes) for 10 randomly selected songs from Sharon’s computer. What is the expected value of T?

• 4.0
• 7.2
• 10.0
• 40.0

The mp3 music files on Sharon’s computer have a mean size of 4.0 megabytes and a standard deviation of 1.8 megabytes. She wants to create a mix of 10 of the songs for a friend. Let the random variable T = the total size (in megabytes) for 10 randomly selected songs from Sharon’s computer. What is the standard deviation of T (assume the lengths of the songs are independent)?

• 1.8
• 3.24
• 5.69
• 18.0

A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. The probability that she makes all of her first four free throws and then misses her fifth attempt this season is

• 0.32768
• 0.08192
• 0.06554
• 0.00128

On a physical fitness test middle school boys are awarded one point for each push-up they can do, and a point for each sit-up. National results showed that boys average 18 pushups with a standard deviation of 4 push-ups, and 34 sit-ups with standard deviation of 11. The mean of their combined (total) scores was therefore 18 + 34 = 52 points. What is the standard deviation of their combined scores?

• 5.3

• 11.7

• 15

• It cannot be determine

Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5 and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?

• 1.708
• 1.848
• 2.415
• 3.416