Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.In what range would you expect to find the middle 68% of most pregnancies

Answer 1

The range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].

Explanation:

We are given that the lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.

Let X = lengths of pregnancies in a small rural village

SO, X ~ Normal(
`\mu=262,\sigma^(2) = 17^(2)`)

Here,
`\mu` = population mean = 262 days

`\sigma` = standard deviation = 17 days

Now, the 68-95-99.7 rule states that;

• 68% of the data values lies within one standard deviation points.

• 95% of the data values lies within two standard deviation points.

• 99.7% of the data values lies within three standard deviation points.

So, middle 68% of most pregnancies is represented through the range of within one standard deviation points, that is;

[
`\mu -\sigma` ,
`\mu + \sigma` ] = [262 - 17 , 262 + 17]

= [245 days , 279 days]

Hence, the range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].