Question

Twenty seven percent of Canadian men over 35 years have high blood pressure. To run an experiment, a researcher needs to identify at least 22 men with high blood pressure. If the researcher examines 100 men over 35 years, what is the approximate probability he or she finds enough men with high blood pressure to run the experiment? Use the normal approximation to the binomial.

Answer 1

X is no of canedian men having high blood pressure

p= 0.27 , n = 100

X has binomial distribution with parameters n=100 and p= 0.27

By using normal approximation

X will follow normal with parameters mu = n*p= 100*0.27 = 27 and sigma = sqrt( n*p*(1-p))

= Sqrt ( 19.71)= 4.44

i.e X has Normal distribution with parameters mu =27 and sigma = 4.44

Now P( X>=22) =

P[ {(x-27)/4.44}>= { (22-27)/4.44}]

i.e. P ( Z>= -1.126)= 1- P ( Z<= -1.13)

= 1- P( Z>= 1.13) = 1- 0.12924= 0.8708

Required probability is 0.8708