Economics 320
Problem Set 1
Probability and Statistics Review
Due Feb 5
1. If two balanced die are rolled what is the probability:
a) that the sum of the two numbers that appear is odd?
b) that the difference between the two numbers that appear
will be less than three?
2. Suppose that two machines 1 and 2 in a factory are operated independently of each other. Let
A be the event that machine 1 will become inoperative during a given 8 hour period; let B be the
event that machine 2 will become inoperative during the same period.
Suppose Pr(A)=1/3 and Pr(B)=1/4.
Find the probability that at least one of the machines will become
inoperative during the given period.
3. In a class of 50 students, the number of students Ni of each age i
is shown:
AGE i Ni
===== ====
18
20
19
22
20
4
21
3
25
1
If a student is to be selected at random from the class, what is
the expected value of her age?
4. Suppose that the measured voltage in a certain electric circuit has
a normal distribution with mean 120 and standard deviation 2.
If a measurement of the voltage is made, what
is the probability that it will lie between 116 and 118?
5. Determine the probability distribution for a random variable, R, that the equals the number of
points showing when a regular six-sided die is rolled once. For this random variable
determine the expected value, the variance and the standard deviation.
6. The Stanford-Binet IQ test has a mean of 100 and a standard deviation of 16. How likely is it
that a randomly chosen person gets a score of at least 140? (Assume that IQ's and test
scores are normally distributed.)
7. A buyer of shirts for a department store wants to test whether shirts with sleeve labels of "33
inches" really meet that specification. A random sample of n=100 from a very large
number of shirts is to be taken; the desired significance level is = .025. The sample
shows a mean length of 34 inches with a standard deviation of 2 inches. Do the test.
Look at the problems at the end of chapters 4 and 5 in Schmidt.