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

Answer:

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

Step-by-step 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].