A report from the Medical College of Georgia stated that the proportion of infants born with Down Syndrome is 0.0011. Assume a sample of 5000 births is studied.

Use the Poisson approximation to the binomial distribution to compute the following:

a. The probability that exactly 5 of the 5000 births involved Down Syndrome

b. The probability that fewer than 4 of the 5000 births involved Down Syndrome

c. The probability that more than 3 of the 5000 births involved Down Syndrome

d. The mean number of births that involved Down Syndrome

e. The standard deviation of the number of births that involved Down Syndrome