Write the binomial probability and the normal probability for the shaded region

Question

Write the binomial probability and the normal probability for the shaded region of the graph. Find the value of each probability and compare the results.

n equals 16n=16

p equals 0.55p=0.55

Write the binomial probability for the shaded region of the graph and find its value. Select the correct choice below and fill in the answer box within your choice.

A.

P(33less than<xless than<77)equals=P(33.5)plus+P(44.5)plus+P(55.5)plus+P(66.5)equals=nothing

B.

P(33less than or equalsxless than or equals77)equals=P(33)plus+P(44)plus+P(55)plus+P(66)plus+P(77)equals=nothing

C.

P(44less than<xless than<66)equals=P(55)equals=nothing

D.

P(44less than or equalsxless than or equals66)equals=P(44)plus+P(55)plus+P(66)equals=nothing

Write the binomial probability and the normal probability for the shaded region of the graph. Find the value of each probability and compare the results.

024681012141600.040.080.120.160.20.24xP(x)

n equals 16n=16

p equals 0.55p=0.55

x y graph

Explanation / Answer

Ans:

Given that

n=16,p=0.55

Binomial probability:

P(x=k)=16Ck*0.55k*(1-0.55)16-k

P(3<=x<=7)=P(x=3)+P(x=4)+P(x=5)+P(x=6)+P(x=7)=0.2553

Normal probability:

mean=16*0.55=8.8

standard deviation=sqrt(16*0.55*0.45)=1.98997

z(2.5)=(2.5-8.8)/1.98997=-3.166

z(7.5)=(7.5-8.8)/1.98997=-0.653

P(-3.166<z<-0.653)=P(z<-0.653)-P(z<-3.166)=0.2568-0.0008=0.2560

Results are approximately same.

x p(x) 3 0.0029 4 0.0115 5 0.0337 6 0.0755 7 0.1318 total 0.2553

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