Assume that the durations (in months) of human pregnancies can be modelled

with the following probability density function:

2-

3

-

4511 -

6

if 0 -

11,

0 otherwise.

a. Determine the constant .

b. What are the modal and the median duration of all human pregnancies?

c. Calculate the average and standard deviation of the durations of all human

pregnancies.

d. What is the probability that in a random group of 40 pregnant women there

will be more than 30 women whose pregnancies last longer than 8 months?