Question

An insurance policy costs ​$110 and will pay policy holders $12,000 if they suffer a major injury​ (resulting in​ hospitalization) or $3500 if they suffer a minor injury​ (resulting in lost time from​ work). The company estimates that 1 in every 1985 policy holders will suffer a major injury and that 1 in 468 will suffer a minor injury.

​a) Create a probability model for the profit on a policy.

​b)​ What's the​ company's expected profit on the​ policy?

​c)​ What's the standard​ deviation?

Answer 1

a) below is pmf of expected payout:

P(X=110-12000=-11890)= 1/1985 =0.000504
P(X=110-3500=-3390)=1/458=0.002137

P(X=110) =1-0.000504-0.002137 =0.997359

from above :

	x	P(x)	xP(x)	x^2P(X)
major injury	-11890	0.000504	-5.989924433	71220.20151
minor injury	-3390	0.002137	-7.243589744	24555.76923
no injury	110	0.997359	109.7095416	12068.04958
		total	96.48	107844.02

b)company's expected profit E(X) =$96.48

c) E(X²) =107844.02

hence std deviation =(E(X²)-(E(X))²)^1/2 =(107844.02-96.48²)^1/2=313.905