Question

Use R instead of a calculator for Questions 5 and 6. Please attach the R commands output and graphs that you used to answer the question. The R output alone is not an answer to the question. Please write a sentence or two to properly answer each question. Assume that the distribution of the duration of human pregnancies can be approxi- mated 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 r 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 (e) We select 60 pregnant women at random. What is the probability that the average (f) If the duration of a human pregnancy is not normally distributed (in fact it is duration of these 10 pregnancies will be less than 260 days? duration of these 60 pregnancies will be less than 260 days? 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