Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. In what range would you expect to find the middle 50% of most pregnancies? Between and . If you were to draw samples of size 36 from this population, in what range would you expect to find the middle 50% 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

Explanation:

Given that the lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days.

X is N(267,17) where x = length of pregnancies in days

For middle 50% we must have on either side 25% area

Hence z= ±0.675

Corresponding x score would be

`267-0.675(17), 267+0.675(15)\\=(255.525,278.475)`

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Sample size = n =36

Std error of sample =
`(17)/(√(36) ) =2.83`

50% would be within

`267-0.675(2.83), 267+0.675(2.83)\\=(265.09,268.91)`

=between 265.1 and 268.9