Question

9. Assume that 1% of men under 20 experience hair loss and that 10% of men over 30 experience hair loss. A sample of 20 men under 20 and 30 men over 30 are examined.What is the probability that four or more men experience hair loss?

Answer 1

Solution:

From the question, we can observe that it is poisson approximation of a sum of binomial random variables with n1 = 20, p1 = 0.01 and n2 = 30, p2 = 0.10

Mean, = n1p1 + n2p2

= 20 (0.01) + 30 (0.10)

= 3.2

Using Poisson distribution formula, we have

P (X = x) =

P (X 4) = 1 - P (X < 4)

= 1 - [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)]

= 1 - [e^-3.2 (3.2)^0/0! + e^-3.2 (3.2)^1/1! + e^-3.2 (3.2)^2/2! + e^-3.2 (3.2)^3/3!]

= 1 - [0.0408 + 0.1304 + 0.2087 + 0.2226]

= 1 - 0.6025

= 0.3975

Hence the probability that four or more men experience hair loss is 0.3975.