Question 1:

Compute the mean and standard deviation of the random variable with the given discrete probability distribution.

x	Px
6	0.17
2	0.07
2	0.24
4	0.28
6	0.24

(a) Find the mean. Round the answer to three decimal places, if necessary.

(b) Find the standard deviation. Round the answer to three decimal place, if necessary.

Question 2:

Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let

X

be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of

X

is given by

x	0	1	2	3	4
Px	0.32	0.39	0.17	0.08	0.04

(f) Compute the standard deviation x. Round the answer to three decimal places.

Question 3:

Relax! A recent survey asked

1669

people how many hours per day they were able to relax. The results are presented in the following table.

Number of Hours	Frequency
0	112
1	185
2	336
3	249
4	315
5	229
6	150
7	33
8	60
Total	1669

(a) Construct the probability distribution of X. Round the answer to three decimal places.

x	0	1	2	3	4	5	6	7	8
P ( x )

(b) Find the probability that a person relaxes more than 5 hours per day.

The probability that a person relaxes more than 5 hours per day is Blank .( Round the answer to three decimal places.)

(c) Find the probability that a person doesn't relax at all.

The probability that a person doesn't relax at all is Blank.( Round the answer to three decimal places.)

(d) Compute the mean x . Round the answer to two decimal places.

(e) Compute the standard deviation x . Round the answer to three decimal places.

Question 4:

Craps: In the game of craps, a pair of dice are rolled, and people bet on the outcome. For example, you can bet $1 that the sum of the dice will be 3 (also called "Ace Deuce"). The probability that you win is 118 , and if you win, your profit is $15. If you lose, you lose $1.

(a) What is the expected value of your profit? Round the answer to two decimal places.

The expected value of profit is blank dollars.

(b) Is it an expected gain or an expected loss?