In a clinical trial of the allergy drug Nasonex 2103 adult p

In a clinical trial of the allergy drug Nasonex, 2103 adult patients were treated with Nasonex and 14 of the developed viral infections.

Assuming that the same proportion of viral infections applies to all adults who use Nasonex, find the probability that among 5000 randomly selected adults who use Nasonex, at least 40 develop viral infections. (Use normal approximation if applicable, otherwise, answer none of the above.)

a) 0.1210

b) 0.8880

c) 0.0080

d) 0.1120

e) 0.7790

f) None of the above

Solution

As the proportion is assumed same across the population, the number of adults who develop viral infections (X) follows binomial (5000, 14/2103) distribution

n=5000

p = 14/2103 = 0.00666

Using normal approximation for X with mean = np = 5000*0.00666 = 33.2858 and variance = np(1-p) = 33.0642

P(X>=40) = P(Z>= (40-33.2858)/root(33.0642) ) = P(Z>= 1.1677) = 0.1210

Answer: a. 0.1210