Question

Using the program R, Assume that the distribution of the duration of human pregnancies can be approximated with a normal distribution with a mean of 266 days and a standard deviation of 16 days.

(a) What percentage of pregnancies should last between 260 and 280 days?

(b) Find a value x such that 10% of the pregnancies of a duration that is longer than x days.

(c) We select 500 pregnant women at random. Let N be the number of pregnancies in the sample with a duration between 260 and 280 days. Compute P(200 ? N ? 300) and P(N = 265).

(d) We select 10 pregnant women at random. What is the probability that the average duration of these 10 pregnancies will be less than 260 days?

(e) We select 60 pregnant women at random. What is the probability that the average duration of these 60 pregnancies will be less than 260 days?

(f) If the duration of a human pregnancy is not normally distributed (in fact it is highly skewed to the left), how does this impact your answers to (d) and (e)? (Explain in words. No computations are necessary for this question.)

Answer 1