Question

. A new medical test provides a false positive result for Hepatitis 2% of the time. That is, a perfectly healthy subject being tested for Hepatitis will test as being infected 2% of the time. In research, the test is given to 30
healthy (not having Hepatitis) subjects. Let X be the number of subjects who test positive for the disease.

a) What is the probability that all 30 subjects will appropriately test as not being infected?

b) What are the mean and standard deviation of X?

c) To what extent do you think this is a viable test to use in the field of medicine? (3 points)

Answer 1

Here's my first take: Defining a "success" as being a false positive result (that is, the test states that someone has hepatitis when in fact he/she does not), the probability of "success" is 0.02. Since each person is independent of every other person, every test and every set of test results is independent. We administer the test to n = 30 individuals.

Thus, p(success) = p = 0.02, and n = 30. What kind of probability distribution do you think we have here?

Answer 2

Binomial distribution

Answer 3

OK. I think so too.

So: we have a binomial distribution with n = 30 (number of samples) and p = 0.02 (probability of success).

What is the probability of getting zero "successes" here?
There are various ways of calculating this probability:

(1) using a table of binomial probabilities
(2) using a calculator, such as the TI-83 or -84
(3) using the formula for binomial probability

What do YOU choose as your method of obtaining this binomial probability?

Answer 4

np=

mean is 5455 or 0.55
SD== 0.7668 or 0.77

Answer 5

If you calculate np, you are calculating the MEAN.

But you haven't yet calculated the probability of getting zero false positives.

do you have a TI-83 or -84 calculator?

Answer 6

no

Answer 7

How have you calculated binomial probability in the past, without using a calculator?