Question

Records of a health insurance company show that 30% of its policyholders over 50 submit a claim during the year. 15 policyholders over 50 are selected at random; what is the probability that at least 10 will submit a claim during the year? 

What is the probability that 4 will submit a claim during the year?

 How many do you expect to submit a claim?

What is the standard deviation?

Answer 1

This is a binomial distribution with n=15, p=0.3.

$P(X\ge10)=\Sigma_{i=10}^{15}P(X=i)=\Sigma_{i=10}^{15}C_{15}^i0.3^i(1-0.3)^{15-i}=0.0037.$

$P(X=4)=C_{15}^40.3^4(1-0.3)^{11}=0.2186.$

$E(X)=np=15*0.3=4.5.$

$\sigma=\sqrt{np(1-p)}=\sqrt{15*0.3*0.7}=\sqrt{3.15}=1.7748.$