Question

Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 400 policyholders is selected. What is the standard deviation of the sampling distribution of the sample proportion of policyholders filing claims involving theft or robbery from their homes?

		0.1
		0.9
		0. 015
		1.5.

Answer 1

here size of the sample=n=400

Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes.

hence sample proportion of policyholders filing claims involving theft or robbery from their homes=p=10%=0.1

let X be the number of policyholders files involving theft or robbery of personal property from their homes.

so X~Bin(400,0.1) and p=X/400

so variance is

V[X]=400*0.1*(1-0.1)

or V[p]=V[X/400]=400*0.1*0.9/400²=0.1*0.9/400

so standard deviation is sqrt[V[p]]=sqrt(0.1*0.9/400)=sqrt(0.000225)=0.015 [answer]