The length of human pregnancy from conception to birth can be modeled as a distribution that is fairly normal with a mean of 266 days and standard deviation 16 days. Please answer the following questions.

a) What will be the shape the distribution. Calculate in days, the values of the relevant variable at1,2, and3 standard deviations from the mean.

b) According to this model, what percentage of human pregnancies last longer than 280 days? Pleaseinterpret your answer.

c) Approximately 7 % of infants are premature. Using this model, find the pregnancy time thatwould result in a premature birth. Please interpret your answer.

d) A random sample of 16 individuals is selected from the population of pregnant woman. Let X be the average pregnancy length of these 16 individuals. What will be nature the distribution of X and its two parameters. Explain in brief.

e) What is the probability that the 16 individuals in part (d) will have an average pregnancy length longer than 275 days?