The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 17 days.

Question

In what range would you expect to find the middle 95% of most pregnancies? 

Between  ____ and .____

If you were to draw samples of size 31 from this population, in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample? 

Between ___ and .____

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

Answer 1

The middle 95% of the pregnancies are within two standard deviations of the mean: 268 +-/ 2*17 = 234, 302

The middle 95% of the average length of pregnancies' would be a 95% CI: mean +/- z-critical * standard deviation/square root(sample size) = 268 +/- 1.96*17/sqrt(31) = 262,274.