(a) A standard test for gout is based on the serum uric acid level. probabilitys?

(a) A standard test for gout is based on the serum uric acid level. probabilitys?(a) A standard test for gout is based on the serum uric acid level. The level is approximately normally distributed with a mean 5.0mg/100ml and a standard deviation 1.0mg/100ml among healthy individuals and with mean 8.5mg/100ml and standard deviation 1.0mg/100ml among individuals with gout.
Suppose we diagnose people as being healthy if their serum uric acid level is less than 6.75mg/100ml and as having gout if the level is more than 6.75mg/100ml.

(i) What is the probability of a person with gout being correctly diagnosed? (5 marks)

(ii) What is the probability that a healthy person will be diagnosed as having gout? (5 marks)

(iii) If 30 healthy people take the test in a given week, what is the probability that exactly three people will be diagnosed as having gout in that week?(5 marks)

Julius N
(i)
for people with gout, P(X>6.75) is probability of being diagnosed with gout:
z= ( x - µ ) / σ:
x= 6.75-->z= -1.75;
P(X>6.75 )= P(z> -1.75)=0.959941 = 96%

(ii)
for normal people
z= ( x - µ ) / σ: x= 6.75-->z= 1.75;
P(X>6.75 )= P(z> 1.75)=0.040059 = 4%

(iii) using the binomial distribution here are some of the various probabilities:

Binomial Distribution: n= 30 p= .040059 µ = 1.20177 ; σ = 1.074071
-- X -- P(X) -------- Σ P(X)
0: 0.293316323, 0.293316323,
1: 0.367208777, 0.660525100,
2: 0.222196196, 0.882721297,
3: 0.086542405, 0.969263702,
4: 0.024377451, 0.993641154,
5: 0.005289897, 0.998931050,

so the P(exactly three normal people getting diagnosed as having gout) = 0.086542405 = 9%

Add your own answer in the comments! Gout - information, symptoms and treatments. Googout.info health information factsheet - advice on gout and its symptoms, causes and treatment, plus prevention through diet.

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