Blood diamonds. According to Global Research News

(Mar. 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. In a random sample of 1,000 rough diamonds purchased by a diamond buyer, let x be the number that are blood diamonds.

a. Find the mean of x.

b. Find the standard deviation of x.

c. Find the z-score for the value x = 280.

d. Find the approximate probability that the number of the 1,000 rough diamonds that are blood diamonds is less than or equal to 280.

c. Find the z-score for the value x = 810.

d. Find the approximate probability that the number of Cesarean sections in a sample of 1,000 births is less than or equal to 810.