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A study studied the birth weights of 1,600 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number. Hint: Use the empirical rule. Answer:

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JeanaShupp

Answer: 1527

Step-by-step explanation:

Given: Mean : [tex]\mu = 3234\text{ grams}[/tex]

Standard deviation : [tex]\sigma=871\text{ grams}/tex]

Sample size : [tex]n=1600[/tex]

The formula to calculate the z score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X=1492

[tex]z=\dfrac{1492-3234}{871}=-2[/tex]

The p-value of z =[tex]P(z<-2)=0.0227501[/tex]

For X=4976

[tex]z=\dfrac{4976-3234}{871}=2[/tex]

The p-value of z =[tex]P(z<2)=0.9772498[/tex]

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

[tex]P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997[/tex]

Now, the number  newborns who weighed between 1492 grams and 4976 grams will be :-

[tex]1600\times0.9544997=1527.19952\approx1527[/tex]

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