Problem 6 [12 Pts]

A clinic plans to set up a mass testing program for diabetes using an inexpensive test of high reliability:

of all people with diabetes, 95% are correctly diagnosed positive (as having diabetes): of all people free of

diabetes, 98% are correctly diagnosed negative (the remaining 2% being erroneously diagnosed positive).

The community served by the clinic has about 10,000 patients, and the undiagnosed diabetes rate runs at

about 1%. The clinic director wants to know three things:

(a)

(3 pts) About how many patients will have diabetes and be missed (i.e. get a negative diagnosis)?

(b)

(3 pts) About how many patients will be diagnosed positive (and therefore require follow up)?

(c)

(3 pts) What proportion of the patients in part (b) will actually have diabetes?

(d)

(3 pts) The director cannot believe your answer to part (c). Explain why it is so low, as simply as you

can.