1 A standard test for gout is based on the serum uric acid l

1. A standard test for gout is based on the serum uric acid level. The level is approximately Normally distributed with mean 5.0 mg/100 mL and standard deviation 1.0 mg/100 mL among healthy individuals and with mean 8.5 mg/100 mL and standard deviation 1.0 mg/100 mL among individuals with gout.
Suppose we diagnose people as being healthy if their serum uric acid level is less than 6.75 mg/100 mL and as having gout if the level is more than 6.75 mg/100 mL.
(a) What is the probability that a person with gout will be diagnosed as healthy? [2 marks]
(b) What is the probability that a healthy person will be diagnosed as having gout? [2 marks]
(c) If 50 healthy people take the test in a given week, what is the distribution of X, the number of healthy people diagnosed as having gout in that week? [2 marks]
Suppose we now wish to change the serum uric acid level used to diagnose gout.
(d) What should the level be if 90% of people with gout are to be correctly diagnosed? [2 marks]
(e) At this level, what proportion of healthy people will be diagnosed as having gout? [2 marks]

i can\'t understand (d),(e) problems

Solution