The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with an average weight of 5 lbs and a standard deviation of 2 lb. If a newborn baby boy, born at the local hospital, is randomly selected, find the probability that the weight of the newborn baby boy will be between 5 lbs and 11 lbs.

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-08T06:45:46+02:00

Answer: 0.4987

Step-by-step explanation:

Given : The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with

Mean : [tex]\mu=5\text { lbs}[/tex]

Standard deviation : [tex]\sigma= 2\text{ lbs}[/tex]

Let X be the random variable that represents the weight of randomly selected student .

Z score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 5 lbs

[tex]z=\dfrac{5-5}{2}=0[/tex]

For x = 11 lbs

[tex]z=\dfrac{11-5}{2}=3[/tex]

By using the standard normal distribution table , the probability that the weight of the newborn baby boy will be between 5 lbs and 11 lbs :-

[tex]P(5<X<11)=P(0<z<3)=P(z<3)-P(z<0)\\\\=0.9986501-0.5=0.4986501\approx0.4987[/tex]

Hence, the probability that the weight of the newborn baby boy will be between 5 lbs and 11 lbs =0.4987