A group of realtors esitmates that 23 of all homes purchase

A group of realtors esitmates that 23 % of all homes purchased last year were considered investment properties. If a sample of 800 homes sold last year is obtained, what is the probability that at most 200 homes are going to be used as investment property? (Round answer to four decimal places)

a. 0.0901

b. 09099

c. 0.5935

d. 0.4066

Solution

mean=n*p=800*0.23=184

standard deviation =sqrt(n*p*(1-p))

=sqrt(800*0.23*(1-0.23))

=11.90294

So the probability is

P(X<=200) = P((X-mean)/s <(200-184)/11.90294)

=P(Z<1.34) =0.9099 (from standard normal table)

Answer: b. 09099