AP Stats
Linear Combinations
Name________________________
1. A college uses SAT scores as one criterion for admission. Experience has shown that the
distribution of SAT scores among its entire population of applicants is such that
SAT Math score (X)
 x  519
 x  115
SAT Verbal score (Y)
 x  507
 x  111
What are the mean and standard deviation of the total score among students applying to
this college?
2. Laboratory data show that the time required to complete two chemical reactions in a
production process varies. The first reaction has a mean time of 40 minutes and a
standard deviation of 2 minutes; the second has a mean time of 25 minutes and a
standard deviation of 1 minute. The two reactions are run in sequence during production.
There is a fixed period of 5 minutes between them as the product of the first reaction is
pumped into the vessel where the second reaction will take place. What is the mean time
required for the entire process? What is the standard deviation?
3. Find the mean and standard deviation for each of these variables:
X
Y
Mean
10
20
St. Dev.
2
5
A. 3X
B. Y+ 6
C. X + Y
D. X – Y
4. Find the mean and standard deviation for each of these variables:
Mean
80
12
X
Y
St. Dev.
10
3
A. x – 20
B. 0.5Y
C. X + Y
D. X – Y
E. 3X + Y
F. 5X – 2Y
5. Answer the following for the distributions shown below:
x
2
3
4
5
p(x)
0.2
0.3
0.1
0.4
y
4
8
12
16
p(y)
.37
.22
.17
.24
a. Find the mean and standard deviation for both and fill them into the appropriate place
on the chart below:
Mean
St. Dev
x
y
b. Find 3 x  2 y
c. Find  3 x  2 y
d. Find  x  y
e. Find  x  y
f.
g. Find  3 x 5
Find 3 x 5