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STAT 302H Midterm Exam #1 Spring 2007
1. Many characteristics are inherited as a result of the genetic make-up of an offspring’s two
parents and the environmental exposures experienced during prenatal development. Birth
weight is one of these characteristics. The table below lists the probability distribution
for birth weights (in pounds) of children that go to full term before delivery.
Birth Weight Probability
5.00- 5.99 0.05
6.00- 6.99 0.10
7.00- 7.99 0.30
8.00- 8.99 0.34
9.00- 9.99 0.14
10.00-10.99 0.04
11.00-11.99 0.02
12.00-12.99 0.01
a. Find the mean birth weight.
b. What is the probability of a child being born with a birth weight greater of at
least 8 lbs?
c. How would you expect the probability distribution for children who were born
prematurely to differ from the distribution given in this problem? Why?
2. I am interested in determining what proportion of people in Texas support the ban of the
use of federal money for stem cell research. Before I run my study, I would like to see
what the probability of certain types of results might be if I am correct about the true
proportion of the population who support the ban. It is my contention that only 25% of
the state support the ban.
a. Assuming I run a study asking 15 people, what would be the probability that no
one person supports the ban?
b. Assuming I run a study asking 15 people, what would be the probability that at
most one person supports the ban?
c. Assuming that I run a study with 1,000 people instead of 15, what would be the
probability that less than half the people support the ban?
3. Although the high tide levels on the Texas coast are quite small, it is still very important
to determine them accurately because the average high tide level is used to determine the
property line along the coast and, thus, the oil rights associated with the property. High
tide levels can be sampled to estimate the average high tide for a property, and the levels
are measured in inches above normal.
a. Assuming that I need a 95% confidence interval to have a width of 2.5 inches to
produce a sufficiently accurate estimate to make a legal claim, what size sample
should I take if the variance of the high tide levels is 30?
b. Assume for this part that I did not use any of the information in part (a), but
instead just took a sample of five high tide levels and got the following five
values: 5, 22, 15, 20, 12. Find a 95% confidence interval for the mean high tide
level.
c. I claim is that my property’s average high tide level is 7 inches. Do the data in
part (b) support my claim? Are you comfortable with your conclusion? Why?
