Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 12 days.

In what range would you expect to find the middle 68% of most pregnancies?
Between __ and ___ .

If you were to draw samples of size 48 from this population, in what range would you expect to find the middle 68% 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

Solution:

Given a bell shaped distribution( NORMAL DISTRIBUTION) with

= 264

= 12

1)

According to the empirical rule , 68% of the data lie within 1 standard deviations from the mean

i.e. between - and +

i.e. between 264 - 12  and 264 + 12

Between 252 to 276

2)

n = 48

The sampling distribution of the is approximately normal with

Mean = = 264

SD =       = 12/​48 =  1.73201

- = 264 - 1.73201 = 262.267945

+ = 264 + 1.73201 = 265.73201

Answer : between 262.3 and 265.7