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

The probability of a true positive is 1.00 - 0.02 = 0.98
The probability that 30 healthy subjects will test as not being infected is given by:
\[(0.98)^{30}=you\ can\ calculate\]

Answer 2

(0.98)^30=29.4

Answer 3

Not really. You have multiplied 0.98 by 30, however (0.98)^30 means 0.98 multiplied by itself 30 times.

Answer 4

not understanding what you are saying

Answer 5

0.54548

Answer 6

For example:
\[(0.98)^{5}=0.98\times0.98\times0.98\times0.98\times0.98=0.90392\]

Answer 7

You are correct in calculating the required probability to be 0.54548.

Answer 8

where did (0.98)^5 came from

Answer 9

That was an example to show you the meaning of raising 0.98 to a power (the power of 5 as an example). Of course solving the problem requires 0.98 to be multiplied by itself the appropriate number of times which you did to get the correct answer of 0.54548.

Answer 10

ok at first I put it the calculator wrong

Answer 11

so a) is 0.54548

Answer 12

into calculator

Answer 13

(b) The mean is given by:
\[np=30\times0.98=you\ can\ calculate\]
The standard deviation is given by:
\[\sqrt{np(1-p)}=\sqrt{30\times0.98\times0.02}=you\ can\ calculate\]

Answer 14

mean= 29.4 and sd=0.10

Answer 15

or is it 0.11

Answer 16

I think it is a viable test use in the field of medicine because of the result from the probablility.

Answer 17

The s.d. is 0.7668.

Answer 18

mean is 6

Answer 19

The mean of X is np = 30 * 0.98 = 29.4