Suppose the birth weight in a local community is approximately normal with . µ=7

Question

Suppose the birth weight in a local community is approximately normal with . µ=7.8 lbs and the ?=1.9 lbs .

What is the 20th percentile of the birth weight?

What is the probability of finding a new born weighing at least 6.5 lbs?

What proportion of newborns will have their birth weight to be between 6.5 and 8.0 lbs, the healthy birth weight range according to the national standards?

In a sample of 60 babies what is the probability that the mean birth weight is more than 6.5 lbs?

Really struggling on this problem! Please help.

Explanation / Answer

Ans:

Given that

µ=7.8 lbs and ?=1.9 lbs

1)P(Z<=z)=0.2

z=normsinv(0.2)=-0.8416

P20=7.8-0.8416*1.9=6.20

2)

z=(6.5-7.8)/1.9

z=-0.684

P(z>=-0.684)=0.7531

3)

z(8)=(8-7.8)/1.9=0.105

P(-0.684<z<0.105)=P(z<0.105)-P(z<-0.684)

=0.5419-0.2469=0.2950

4)

z=(6.5-7.8)/(1.9/sqrt(60))

z=-5.30

P(z>-5.30)=1

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