Assume that the distribution of the duration of human pregna

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.

(c) 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?

(d) 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, does that change your answers to parts (c) and (d)? Explain why or why not in each case.

already found answers for parts c and d, need answer to part f only please

c: 0.1178

d:0.0018

Solution

It wont change answer to (d) because of central limit theorem, which states that for large sample size (30 or above) the sample mean is approximately normal. Answer to (c) will become invalid, and we cannot calculate it.