E) A random number generator is set to generate single digits between 0 and 9. One hundred and fifty
random numbers are generated. The probability distribution for this random number generator is
given below. What is the mean of this distribution?
x       0      1       2        3        4        5         6        7          8         9
P(x)  0.09  0.12  0.11   0.08    0.09   0.13    0.10    0.07    0.10    0.11

 

A) 5         B) 6.6          C) 7           D) 4.5

 

 

 

F)  In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2, 3, 4,
5, or 6 then the person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10,
11, or 12 then the person gets nothing (loses $2). If the total of the two dice is 7, the person gets
$0.75 back (loses $0.25). What is the expected value of playing the game once?

A) $0.00           B) $2.00         C) -$0.42            D) -$0.04

 

 

 

 

G) In the American version of the Game Roulette, a wheel has 18 black slots, a8 red slots and 2 green
slots. All slots are the same size. In a carnival game, a person wagers $2 on the roll of two dice. A
person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on
either red or black and that color comes up, they win $10 otherwise they lose their wager. What is
the expected value of playing the game once?

A) $0.50       B) -$0.26           C) $0.26           D) -$0.50

 

 

 

 

H) The random variable x represents the number of credit cards that adults have along with the
corresponding probabilities. Find the mean and standard deviation for the random variable x.
x     P(x)
0     0.49
1     0.05
2     0.32
3     0.07
4     0.07

A) mean: 1.39; standard deviation: 0.80        B) mean: 1.18; standard deviation: 1.30
C) mean: 1.39; standard deviation: 0.64        D) mean: 1.18; standard deviation: 0.64

 

 

 

I) A basketball player is asked to shot free throws in sets of four. The player shoots 100 sets of 4 free
throws. The probability distribution for making a particular number of free throws id given below.
Determine the standard deviation for this discrete probability distribution.
x              0              1             2              3              4
P(x)       0.02          0.07         0.22          0.27       0.42

A) 1.21       B) 0.28        C) 1.05         D) 1.10