Question

The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days.

A) What percentage of pregnancies last between 250 and 282 days?
B) Between what values do the lengths of the middle 95% of all pregnancies fall?

Answer 1

A) 68.33%

B) (234, 298)

Explanation:

We have that the mean is 266 days (m) and the standard deviation is 16 days (sd), so we are asked:

A. P (250 x < 282)

P ((x1 - m) / sd < x < (x2 - m) / sd)

P ((250 - 266) / 16 < x < (282 - 266) / 16)

P (- 1 < z < 1)

P (z < 1) - P (-1 < z)

If we look in the normal distribution table we have to:

P (-1 < z) = 0.1587

P (z < 1) = 0.8413

replacing

0.8413 - 0.1587 = 0.6833

The percentage of pregnancies last between 250 and 282 days is 68.33%

B. We apply the experimental formula of 68-95-99.7

For middle 95% it is:

(m - 2 * sd, m + 2 * sd)

Thus,

m - 2 * sd <x <m + 2 * sd

we replace

266 - 2 * 16 <x <266 + 2 * 16

234 <x <298

That is, the interval would be (234, 298)