2. A cohort study investigated the relationship between
cholesterol levels and the risk of coronary heart disease. Investigators
studied 250 people at high risk for heart disease between the ages of 50-59,
following them for 10 years. A hundred people were on a low cholesterol diet
compared to 150 people on a high cholesterol diet. After 10 years the number of
people who had coronary events were recorded and coded as heart disease (yes vs
no). The SAS table output below summarize the findings. Based on this table
answer the following questions:

a. What percentage of individuals who had heart disease were on a
low cholesterol diet?

b. What percentage of individuals who ate a high cholesterol diet
had evidence of heart disease?

c. What is the odds of heart disease among those on a low
cholesterol diet?

d. What is the odds of heart disease among those on a high
cholesterol diet?

e. What is the odds ratio for the risk of heart disease among
those on a high cholesterol diet compared to a low cholesterol diet?

3. When I visit the local library, the probability that someone is
reading the current issue of US is 0.4, the probability that someone is
reading Time is .3, and the probability that at least one is being read
by someone is .5.

a)
I am planning on going to the library and taking both of them
immediately. What is the probability that both magazines are being read?

b) What is the probability that
neither of the two is being read?

c) What is the probability that
exactly one is being read?

4. Suppose that in a city 37% of the voters are registered
Democrats, 29% are registered Republications, 11% are members of other parties
(e.g Green party etc) and the remaining are not aligned with any party, called
Independents.

a. What is the probability a single randomly selected person from
this city is an Independent voter?

b. Suppose you conduct a poll by calling 5 randomly selected
registered voters, what is the probability that exactly three are Republicans?
(hint: Binomial)

c. What is the probability of no Democrats out of 5 randomly
selected registered voters?

d. What is the probability of at least one Independent voter out
of 5 randomly selected registered voters? (hint: Binomial)

e. Suppose a polling organization calls 1000 registered voters,
how many on average do we expect to be Independent voters?

e. Suppose a polling organization calls 1000 registered voters,
how many on average do we expect to be Democratic voters?

5. 56% of all American workers
have a workplace retirement plan, 68% have health insurance and 49% have both
benefits. We select a worker at random

a.
What is the probability that they have neither
plan (health insurance nor retirement)

b.
What is the probability they have either
health insurance or a retirement plan?

c.
What is the probability they have ONLY a
retirement plan?

d.
Are having a retirement plan and a health
insurance plan mutually exclusive? Explain.

e.
Are having a retirement plan and a health
insurance plan independent? Explain.

6. A soft drink company holds a
contest in which a prize may be revealed on the inside

of the bottle cap. The probability
that each bottle cap reveals a prize is 0.2, and

winning is independent from one bottle
to the next. You buy three bottles. Let X= number of winning bottles out of 3
tries

(a) What is the sample space of X? In
other words, what are all the possible values of X that you could see?

(b) Find the probability that none of
your bottles reveals a prize.

(b) Find the probability that exactly
1 of your bottles reveals a prize.

(c) Find the probability that you win at least one prize.

(d) Can X be considered arising out of a Binomial distribution? If
so what are n and π? And list all the characteristics that makes it compatible
with this type of probability distribution.

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