according to a recent national health statistic report the weight of male babies less than 2 months old is in the U.S is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds

a) what proportion of babies weigh less than 15 pounds

b) what proportion of babies weigh between 13 and 15 pounds

c) is it unusual for a baby to weigh more than 17 pounds

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frika frika · Answer 1 · 2018-10-14T22:13:12+02:00

The mean [tex]\mu =11.5[/tex] pounds;

the standard deviation is [tex]\sigma =2.7[/tex] pounds.

Let the variable [tex]X[/tex] be the weight of male babies less than 2 months old. It is normally distibuted with a law

[tex]X\sim N(11.5, 2.7^2).[/tex]

Find the variable

[tex]Z=\dfrac{X-\mu}{\sigma},[/tex] that is normally distributed with a law

[tex]Z\sim N(0, 1).[/tex]

Part A.

If X=15 pounds, then

[tex]Z=\dfrac{15-11.5}{2.7}\approx 1.2963[/tex] and

[tex]Pr(X<15)=Pr(Z<1.2963)\approx 0.9032[/tex]

Part B.

If X=15 pounds, then

[tex]Z=\dfrac{15-11.5}{2.7}\approx 1.2963.[/tex]

If X=13 pounds, then

[tex]Z=\dfrac{13-11.5}{2.7}\approx 0.5555[/tex] and

[tex]Pr(13<X<15)=Pr(0.5555<Z<1.2963)\approx 0.9032-0.7123=0.1909[/tex]

Part C.

If X=17 pounds, then

[tex]Z=\dfrac{17-11.5}{2.7}\approx 2.0370[/tex] and

[tex]Pr(X>17)=Pr(Z>2.0370)=1-Pr(Z<2.0370)\approx 1-0.9793=0.0207.[/tex]

This means that approximately 2% of babies are born with weight more than 17 pounds and, therefore, seems to be quite unusual for a baby.