Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 269 days and a standard deviation of 15 days.

In what range would we expect to find the middle 68% of most lengths of pregnancies? THEN Round the answer to one decimal place.

Between ? and ? days

If we were to draw samples of size 38 from this population, in what range would we expect to find the middle 68% of most averages for the lengths of pregnancies in the sample? THEN Round the answer to one decimal place!

Between ? and ? days

Answer 1

According to empirical ( 68 - 95 - 99.7) rule,

Approximately, 68% data falls in 1 standard deviation of the mean.

That is between - and   +

between 269 - 15 and 269 + 15

between 254 and 284

For sample of 38 ,

Approximately, 68% data falls in 1 standard deviation of the mean.

That is between - /sqrt(n) and   + ​​​​​​​/sqrt (n)

between 269 - 15/sqrt(38) and 269 + 15 / sqrt(38)

between 266.6 and 271.4