In Exercise, you learned that 32% of all births in the United States occur by Caesarian section each year (National Vital Statistics Reports, Mar. 2010). In a random sample of 1,000 births this year, let x be the number that occur by Caesarian section.

a. Find the mean of x.

b. Find the standard deviation of x.

c. Find the z -score for the value x = 200.5.

d. Find the approximate probability that the number of Caesarian sections in a sample of 1,000 births is less than or equal to 200.