Question

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:

Answer 1

Answer: 1527

Explanation:

Given: Mean :
`\mu = 3234\text{ grams}`

Standard deviation :
`\sigma=871\text{ grams}/tex]</p><p>Sample size : [tex]n=1600`

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

`z=(X-\mu)/(\sigma)`

For X=1492

`z=(1492-3234)/(871)=-2`

The p-value of z =
`P(z<-2)=0.0227501`

For X=4976

`z=(4976-3234)/(871)=2`

The p-value of z =
`P(z<2)=0.9772498`

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

`P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997`

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

`1600*0.9544997=1527.19952\approx1527`