Question

Assume that the duration of human pregnancies can be described by a normal model with a mean 264 days and a standard deviation 18 days.

What percentage of pregnancies should last between 265 and 275 days?

Answer 1

70.52% of pregnancies should last between 265 and 275 days.

Step-by-step explanation:

To find the percentage of pregnancies that should last between 265 and 275 days, we need to find the area under the normal curve between those two values.

First, we need to convert the values to z-scores using the formula:

z = (x - mean) / standard deviation

For 265 days: z = (265 - 264) / 18 = 0.056

For 275 days: z = (275 - 264) / 18 = 0.611

Next, we use a Z-table or a calculator to find the area between these two z-scores.

The percentage can be calculated by subtracting the area to the left of 265 (0.0239) from the area to the left of 275 (0.7291).

So, the percentage of pregnancies that should last between 265 and 275 days is :

0.7291 - 0.0239

= 0.7052, or 70.52%.