Answer to Question #316382 in Statistics and Probability for Bless

Question

The paper “Are Babies Normal?” byT. Clemons

and M. Pagano (The American Statistician, Vol. 53,No. 4, pp.

298–302) focused on birth weights of babies. According to

the article, the mean birth weight is 3369 grams (7 pounds

6.5 ounces) with a standard deviation of 581 grams.

a. Identify the population and variable.

b. For samples of size 200, find the mean and standard

deviation all possible sample mean weights.

c. Repeat part (b) for samples of size 400.

Answer 1

$a:population\,\,is\,\,all\,\,babies, variable\,\,is\,\,baby‘s\,\,weight\\b:\\\mu _{\bar{x}}=EX=3369\\\sigma _{\bar{x}}=\frac{\sigma X}{\sqrt{n}}=\frac{581}{\sqrt{200}}=41.0829\\c:\\\mu _{\bar{x}}=EX=3369\\\sigma _{\bar{x}}=\frac{\sigma X}{\sqrt{n}}=\frac{581}{\sqrt{400}}=29.05$