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

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()

Here, = population mean = 262 days

          = standard deviation = 17 days

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

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

[ , ]  =  [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].

step-by-step :