Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 17 days.

In what range would you expect to find the middle 98% of most pregnancies?


Between ___ and ___ .



If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?


Between ___ and ____ .

Answer 1

(221.39, 300.61) and (255.2223, 266.7777)

Explanation:

Given that X, the lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 17 days

Middle 98% would lie on either side of the mean with probability ±2.33 in the std normal distribution on either side of 0

Corresponding we have x scores as

Between
`261-2.33*17` and
`261+2.33*17`

i.e. in the interval = (221.39, 300.61)

If sample size = 47, then std error of sample would be

`(17)/(√(47) )`

So 98% of pregnancies would lie between

`261-2.33*(17)/(√(47) )` and
`262+2.33*(17)/(√(47) )`

= (255.2223, 266.7777)