In Chelmsford County Hospital, the probability that a randomly chosen birth results in a boy is 45%. Over the course of a month, there are 20 births at the hospital.

a)Is a normal approximation to the binomial distribution appropriate here? Show your calculations and explain your choice.

b)What is the chance that more than 14 of the births are boys? Use the method of the normal approximation to the binomial distribution. Provide evidence of your work by typing out your full solution.

c)What is the chance that more than 14 of the births are boys? Use the binomial distribution formula. Provide evidence of your work by typing out your full solution.