The probability of contracting TB is p 00005 In a town of 8

The probability of contracting TB is p = 0.0005. In a town of 8000 people: What Is the expected number of new cases in a year? What is the probability of having more than 3 cases in a year?

Solution

a)
Expected Number of new cases = Mean ( np ) =8000 * 0.0005 = 4
b)
Standard Deviation ( npq )= 8000*0.0005*0.9995 = 1.9995
Normal Distribution = Z= X- u / sd                   
P(X > 3) = (3-4)/1.9995
= -1/1.9995 = -0.5001
= P ( Z >-0.5) From Standard Normal Table
= 0.6915