Q1: Please complete Parts A-D and ROUND answer as needed.

[ Assume that the duration of human pregnancies can be described by a Normal model with mean 264 days and standard deviation 17 days. a) What percentage of pregnancies should last between 270 and 280 days? b) At least how many days should the longest 15% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care_ to 51 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean, y? Specify the model, mean, and standard deviation. d) What's the probability that the mean duration of these patients' pregnancies will be less than 253 days? a) The percentage of pregnancies that should last between 270 and 280 days is %. (Round to two decimal places as needed.) b) The longest 15% of all pregnancies should last at least days. (Round to one decimal place as needed.) c) Select the correct choice below and, if necessary, ll in the answer box(es) within your choice. O A- A Binomial model with trials and a probability of success of (Type integers or decimals rounded to two decimal places as needed.) O B- A Normal model with mean and standard deviation (Type integers or decimals rounded to two decimal places as needed.) 0 C. There is no model that ts this distribution. d) The probability that the mean duration of these patients' pregnancies will be less than 253 days is (Round to four decimal places as needed.)