How to set up this stats problem

Question

What is the probability a random sample of size 20 will have a mean gestation period within 11 days of the mean?

σ=13

μ=197

Answer 1

So, each person in our sample of 20 from the population will have a gestation period that is normally distributed with mean mu and standard deviation sigma.

 

X_i ~ Normal(197, 13) where i = 1...20

 

That means that the sample mean will have the distribution Normal(197, 13/sqrt(20)). 

 

To find this Probability that the sample mean falls in the interval, we integrate this normal density curve from 186 to 208. 

 

OR we can take the cumulative density for the normal at 208 minus the cumulative density for the normal at 186.