The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 13 days.

Question

In what range would we expect to find the middle 95% of most lengths of pregnancies? Round the answer to one decimal place

Answer 1

Hi Bailey,

I see you have many questions on here and would like to offer you a free one-hour tutoring session to go over these or any other questions you have. I am new to the platform yet have 15+ years of experience directly with Statistics.

Here is the answer to this question:

So, here we are in a rural village where pregnancies are pretty common. People are curious about how long these pregnancies tend to last. Imagine a bell curve that represents the distribution of pregnancy lengths, with most pregnancies falling somewhere in the middle.

Now, we've got two important numbers: the average pregnancy length (which is 268 days) and how much the lengths of pregnancies vary around that average (which is 13 days). This "variation" is what we call the standard deviation. It tells us how spread out the pregnancies are from that average.

To find the range where the middle 95% of these pregnancies lie, we're going to use a handy tool called the Z-score. Think of it as a way to measure how far away from the average a pregnancy length is in terms of standard deviations.

When we're talking about the middle 95%, we're leaving out the extreme 5% on both ends of the bell curve. To do this, we use a Z-score of ±1.96. This value is like a marker that tells us where that 5% cutoff point is.

Now, we're ready to calculate the range. The formula is quite simple: you take the average (268 days) and add and subtract the Z-score (±1.96) multiplied by the standard deviation (13 days).

For the lower limit, it's 268 - (1.96 × 13), and for the upper limit, it's 268 + (1.96 × 13).

After doing the math, we find that the middle 95% of pregnancy lengths in this village should range approximately between 242.2 days and 293.8 days.

So, most pregnancies here last between these two numbers. It's a way to understand the typical range without diving too deep into the statistics.

Hope to review more soon!

Best regards,

Benjamin M.

Answer 2

Hi Bailey,

This problem involves the 68-95-99.7 rule for normal distributions. Under the rule, 68% of the data lies within one standard deviation of the mean, 95% lies within two, and 99.7% lies within three. So, to get the middle 95%, compute

mu +/- 2*sigma where:

mu=mean=268 days

sigma=standard deviation=13 days

Thus:

268-2(13)=242 days

268+2(13)=294 days

The middle 95% will fall between 242 and 294 days.

Good luck. I hope this helps.