Provide answers to the following. Alll WORK MUST BE SHOWN.

(a)It has been reported that the length of human pregnancies from conception to birth approximately follows a normal distribution with a mean of 266 days and a standard deviation of 16 days.

i. Find the probability that the pregnancies will last between 240 to 270 days?

ii. What is the probability that the pregnancies will go beyond 270 days?

iii. What length of time marks the shortest 70% of all pregnancies?

(b)A study on a sample of 60 pregnancies produced a mean of 265 days and a standard deviation of 15.5 days. Find the 95% confidence interval for estimating average length of human pregnancies.