1. A certain Board of Trustees consists of 9 members. Each year, they elect a 3-person
committee to oversee buildings and grounds. When the board elects the buildings and
grounds committee, how many 3 person committees are possible?
2. Given that a woman
PRACTICE EXAM 2
STAT 380
1. The heights of students are normally distributed with a mean of 174.5 centimeters and a
standard deviation of 6.9 centimeters. How many of 1000 students would you expect to have
heights less than 60.0 centimeters?
2. A company
STAT 380
Exam 1
Friday, February 9
1. Suppose we randomly select five recordings of classical music from the
Schwann Record Catalog and determine the listening time for each.
The data values (rounded to the nearest minute) are as listed:
37 46 40 57 200
(
STAT 380/880
Homework 2
1. Assume the pdf of X is given by
(
f (x) =
3 2
27 x
0
for 0 x c
otherwise
a. Find c and verify that this is a pdf.
Solution:
Zc
3 2
x dx c3 = 27 c = 3
27
0
Verify that this is a pdf:
Clearly f (x) 0 for all x
R3
0
3 2
27 x dx
=1
STAT 380/880
Homework 5
due Monday, April 3
1. Use the t-table (Table A.4) to find the following.
a. t.10 when = 12.
Solution: t.10 =1.356.
b. t.025 when = 15.
Solution: t.025 = -2.131.
c. P (T < .906) when = 6.
Solution: P (T < .906) = .80.
2. Use EXCEL
STAT 380/880
Homework 4 Solutions
1. Compute the following probabilities:
a. P (Z 1.75)
Solution: P (Z 1.75) = .9599
b. P (Z > 1.75)
Solution: P (Z > 1.75) = .0401
c. P (Z 1.75)
Solution: P (Z 1.75) = .0401
d. P (.27 Z 1.30)
Solution: P (.27 Z 1.30) = .50
STAT 380/880
Homework 3
1. Let X be a binomial random variable with E(X) = 2 and V ar(X) =
1.6.
a. Find P (X = 2) using the binomial pmf (work out by hand).
Solution: Since E(X) = np = 2 and V ar(X) = np(1 p) = 1.6,
2
8
we find n = 10 and p = .20. Then, P