Combining Random Variables and Expected Value

The mean amount of time to mix the batter for a cake is 14 minutes with a standard deviation of 2.5 minutes. The mean amount of time to bake the cake is 35 minutes with a standard deviation of 6.2 minutes. What is the mean time to make and bake a cake? What is the standard deviation?

• mean = 49 min sd = 8.7 min

• mean = 49 min sd = 6.685 min

• mean = 21 min sd = 8.7 min

• mean = 21 min sd = 6.685 min

The mean hourly salary for a high school graduate is $13.50 per hour with a standard deviation of $5.75. The mean hourly salary for a person with an Associate's degree is $19.75 with a standard deviation of $9.25. What is expected difference in the hourly salaries between a high school graduate and a person who earned an Associate's degree?

• $33.25

• $-3.50

• $-6.25

• $15.00

The mean weight of a bag checked in at Southwest Airlines is 36 pounds with a standard deviation of 3.5 pounds. If two random bags were checked, what is the mean and the standard deviation of the weights of the two bags?

• 36, 4.95

• 36, 7

• 72, 4.95

• 72, 7

The mean weight of a dog is 34 pounds with a standard deviation of 6.7 pounds. The mean weight of a cat is 12 pounds with a standard deviation of 3.1 pounds. If you have 2 dogs and 1 cat, what is the mean and standard deviation of their total weight?

• 80, 9.969

• 80, 16.5

• 46, 7.382

• 46, 16.5

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 that you win. 
Which of the following is the expected value of X?

• $1.00
• $2.50
• $4.00
• $6.00

The table represents the probability of guessing correct on a 5 question true-false quiz.  Find the probability for at least 4 questions correct.

• .03125
• .15625
• .3125
• .1875

Find the missing value for P(X=5) in the probability ditribution:

Number of Toys | Probability

0| 0.03

1| 0.16

2| 0.30

3| 0.23

4| 0.17

5| ?

• 0.11

• 0.21

• 0.01

• 0.31

A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the mean of X + Y?

• 13
• 6.5
• 14
• Not here.

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

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X – Y?

• 24.0

• 17.5

• 12.0

• 6.0

• 4.9