Question

Complete parts​ (a) and​ (b) below.

The number of dogs per household in a small town

Dogs	0	1	2	3	4	5
Probability	0.6740.674	0.2000.200	0.0830.083	0.0230.023	0.0130.013	0.0070.007

​(a) Find the​ mean, variance, and standard deviation of the probability distribution.

Find the mean of the probability distribution.

muμequals=nothing

​(Round to one decimal place as​ needed.)

Find the variance of the probability distribution.

sigma squaredσ2equals=nothing

​(Round to one decimal place as​ needed.)

Find the standard deviation of the probability distribution.

sigmaσequals=nothing

​(Round to one decimal place as​ needed.)

​(b) Interpret the results in the context of the​ real-life situation.

A.A household on average has

0.90.9

dog with a standard deviation of

0.50.5

dog.

B.A household on average has

0.90.9

dog with a standard deviation of

0.90.9

dog.

C.A household on average has

0.50.5

dog with a standard deviation of

0.90.9

dog.

D.A household on average has

0.50.5

dog with a standard deviation of

1515

dogs.

Answer 1

x	P(x)	xP(x)	x2P(x)
0	0.674	0.000	0.000
1	0.200	0.200	0.200
2	0.083	0.166	0.332
3	0.023	0.069	0.207
4	0.013	0.052	0.208
5	0.007	0.035	0.175
	total	0.522	1.122
	E(x) =μ=	ΣxP(x) =	0.5220
	E(x2) =	Σx2P(x) =	1.1220
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.850
	std deviation=	σ= √σ2 =	0.9217

a)

mean of the probability distribution μ=0.5

variance of the probability distribution σ2 =0.85~ 0.9

standard deviation of the probability distribution =0.9

b)

C.A household on average has 0.5 dog with a standard deviation of 0.9 dog.