Question

Assume that newborn girls have birth weights with a mean of 3058 grams and a standard deviation of 704 grams. A random sample of 100 newborn girls is obtained and they have a mean birth weight of 2855 grams. What is the probability of randomly selecting another 100 newborn girls and getting a mean birth weight that is 2855 grams or​ lower? Does it seem like a sample mean of 2855 grams is​ unusual? The probability of getting a mean birth weight that is 2855 grams or lower is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

Answer :

Given that :

Sample size n = 100

Random variable = x

Where X = Birth weights of new born girl.

Mean = E(X) = = 3058

Standard deviation = = 704

So Variance = =

Based on central limit theorem,

~

We already know the formula :

Now we need to find probability of getting a mean birth weight that is 2855 grms or lower is as follows :

= 0.0020