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

Step-by-step explanation:

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

Standard deviation : $\sigma=871\text{ grams}/tex]Sample size : [tex]n=1600$

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

$z=\dfrac{X-\mu}{\sigma}$

For X=1492

$z=\dfrac{1492-3234}{871}=-2$

The p-value of z =$P(z$

For X=4976

$z=\dfrac{4976-3234}{871}=2$

The p-value of z =$P(z$

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

$P(1492$

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

$1600\times0.9544997=1527.19952\approx1527$