Download 1 - Fort Bend ISD

Review
Name: _______________________________
1. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables:
Mean
SD
a. 3X
b. Y + 6
c. 2X + 5Y
d. X – Y
e. X + X
X
10
2
Y
20
5
2. The average length of stay in a hospital is useful for planning purposes. Suppose that the following is the distribution of the length of stay in a hospital after a
minor operation. What is the average length of stay?
Days
2
3
4
5
6
Prob
.05
.20
.40
.20
?
3. Ms. Brown (B) and Mrs. Truong (T) run (OK walk) 2 miles every day. Ms. Brown’s times are normally distributed with mean 39 minutes and standard
deviation of 1 minute. Mrs. Truong is faster but less consistent than Ms.Brown, and her times are normally distributed with mean of 35 minutes and standard
deviation of 2 minutes. On any day, their times are independent of each other. Can Ms. Brown ever beat Mrs. Truong?
a. Find the mean and the standard deviation of difference (D) in their times.
b. The official timekeeper has recently discovered that Ms. Brown’s watch somehow under timed her walk by 2 minutes. What is the expected new time AND
standard deviation for Ms. Brown to walk her 2 miles?
c. Mrs. Truong (the aerobic queen) wants to know the expected number AND variance of calories she will burn off after a 2-mile walk knowing that she burns
25 calories per minute.
4. In a particular game, a marble is randomly chosen from a box that contains 4 red marbles, 1 green marble, and 5 blue marbles. If a red marbles is selected
you win $2, if a green marbles is selected you win $4, and if a blue marbles is selected you win nothing. In the long run, how much money would you expect
to win?
5. Find the mean, variance, and
X
P
-1
0.3
0
0.1
1
0.5
 of X.
Find the mean, variance, and
2
0.1
a. Let W = X - Y. Find the mean, variance, and standard deviation of W.
Y
P
2
0.6

3
0.3
of Y.
5
0.1
b. Let W = -2X + 5Y. Find the mean, variance, and standard deviation of W.
6. Suppose the height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewomen is 66 inches with a standard deviation
of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, what will be the mean and standard deviation for the difference in
heights (male – female) for the set of possible partners? Assume that the heights for policemen and policewomen are independent events.
7. You plan on purchasing a used hummer (don’t even think of a new one). The average sales price is $50,000 with a standard deviation of $5,000. Assume the
world market has influenced the asking price of used hummers to double, what is the new mean and variance of asking price for a used hummer under these
circumstances?
8. The senior class is selling raffle tickets at the Senior Auction and Dinner night. Each raffle ticket costs $10 and they plan on selling 200 raffle tickets. The
prizes, which have been paid for from the money collected from the sale, are one $100 stereo system, two $75 Dillard's gift certificates, four $30 Chili's gift
certificates, and eight $15 AMC gift certificates.
a. What is the expected value of a raffle ticket? (Show the formula, substitutions, and box final answer)
b. How much profit per raffle ticket is the senior class expecting to make?
9. Determine whether the random variable is discrete or continuous.
a. The weight of a newly born kitten.
b. The lifetime of a burning candle.
c. The number of homeless people in the U.S.
Multiple Choice:
X
0
3
6
9
P(X = x)
.3
.4
.1
.2
10. Using the probability distribution table, what is the P(X = 5)?
a) 0.00; 5 does not exist as a possible value for x.
b) 0.50; since it is the mean and median.
c) 0.00; X is a continuous random variable so all ‘=’ probabilities are 0.
d) 0.50; since it falls in the middle.
e) Cannot be determined since the probability table does not contain the needed information.
11. Using the same probability distribution table in the prior problem, what is the P(X < 6)?
a) .1
b) .35
c) .7
d) .8
e) 1.0
12. Using the same probability distribution, what is the expected value and standard deviation of X?
a) 19 and 15.735 b) 19 and 6.946
c) 17 and 6.946
d) 3.6 and 10.44
e) 3.6 and 3.23
A new game of dice is being played with two dice on some college campuses. The dice are rolled one after the other. Instead of adding the numbers on each
die, each player subtracts the number on the second die from the number on the first die. Let S = this difference. (Note that for each die,  = 3.5 and 
1.71.) Assume that rolling the dice are independent events.
13. S consists of the values in which set?
a) {-5, -4, …,4,5}
b) {-6, -5, …, 5, 6} c) {1,2,3,4,5,6}
d) {0,1,2,3,4,5}
14. Assuming that the dice are fair, which of the following is true about the random variable S?
a)  = 0 and   0
b)  = 0 and   1.85
c)  = 0 and   2.41
d)  = 0 and
e)  = 0, but the variance cannot be determined from this information.
e) none of these

 3.42