Question

Will rate!!

Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area, the chance a homeowner is insured against an earthquake is 0.30, A sample of four homeowners are to be selected at random. Suppose X is a random variable that is modeled by a binomial distribution which describes the number of homeowners out of the four that have earthquake insurance. (a) Find the probability mass function of X. (Round your answers to four decimal places.) p(x)

Answer 1

from binomial distribution P(X=x)=⁴C_x(0.3)^x(0.7)^4-x

a)

x	0	1	2	3	4
P(x)	0.2401	0.4116	0.2646	0.0756	0.0081

b)top left curve is right

c) bottom right curve is right

d)

most likely value =1

e)

P(X<=1) =P(X=0)+P(X=1)=0.6517

f)

P(X>=2)=1-P(X<=1)=1-0.6517=0.3483

g)

E(X)=np=4*0.3=1.2

SD(X)=sqrt(np(1-p))=0.92