(4 points) Suppose that the population mean amount of time it takes for a well-trained graduate student to draw a blood sample from the tail vein of a mountain goat is 0.98 minutes, with population standard deviation of 0.661 minutes. Furthermore, suppose that the graduate student's advisor decided to record the amount of time it took for the student to draw blood from 64 mountain goats (i.e., n= 64).

a. (1 point) Let Y bar denote the sample mean time it took to draw a blood sample from these 64 mountain goat. Calculate the standard error of Y bar.

b. (1 point) What is the probability that the sample mean of the amount of time it takes to draw blood from one of these mountain goats is less than 0.9 minutes?

c. (2 points) Suppose we wanted to calculate a 95% confidence interval for the population mean , and that the tolerable error (i.e., W) is one second (that is, 1/60 minutes). What sample size is needed to achieve these specifications? Please show all of your calculations.