Question

A consumer organization inspecting new cars found that many had appearance defects​ (dents, scratches, paint​ chips, etc.). While none had more than three of these​ defects, 9​% had​ three, 15​% had​ two, and 28​% had one defect. Find the expected number of appearance defects in a new car and the standard deviation.

Answer 1

from given data :

x	f(x)	xP(x)	x2P(x)
0	0.4800	0.0000	0.0000
1	0.2800	0.2800	0.2800
2	0.1500	0.3000	0.6000
3	0.0900	0.2700	0.8100
	total	0.8500	1.6900
	E(x) =μ=	ΣxP(x) =	0.8500
	E(x2) =	Σx2P(x) =	1.6900
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.9675
	std deviation=	σ= √σ2 =	0.9836

from above

expected number of appearance defects =0.85

and  standard deviation =0.9836