Homework 7
Due Friday, May 17
1. A beer distributor has a machine in the factor designed to put 12 ounces
of beer in each bottle. Because of slight inconsistencies, the amount
of beer actually put in a bottle follows a normal distribution wiht mean
12.1 ounces and SD .2 ounces.
a) What's the probability that a bottle will have less than 12 ounces?
b) Suppose the distributor wants to ensure that at most 5% of all bottles
have less than 12 ounces. The distributor cannot fix the SD, but by
tinkering with the machinery, they can change the mean. What should the mean
be set at?
c) Assume, again, that the mean amount of beer deposited in a bottle is 12.1
ounces. What's the probability that the average amount of beer in a
six-pack will be less than 12 ounces? In a 12 pack?
2. Chapter 5 (p. 271) 2, 3,7,10, 14
3. Look, once again, at the
Risk data
set. Assume this is a random sample from a normal population.
a) Find a 95% confidene interval for the mean level of risk associated with
flying in a plane.
b) Do people rate risk for flying differently than the risk for living near
a nuclear power plant? Find a 90% confidence interval for the mean
difference. Does it contain zero? What does this fact (that the interval
does or does not contain 0) say about whether people rate these activities
differently?
(Hint: define a new variable plane - nuclear and find a 90% CI for its mean.)
c) What do you think about our assumption that the sample comes from a normal
population? why?