!!! PLEASE HELP !!!

1. The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is one of the busiest in the world with an average of 60 births per day. Let X = the number of births in an hour.

a) Find the mean and standard deviation of X.

b) What is the probability that the maternity ward will deliver three babies in one hour?

c) What is the probability that the maternity ward will deliver at most three babies in one hour?

d) What is the probability that the maternity ward will deliver more than five babies in one hour?

e) Why does this follow a Poisson distribution?

f) State the parameters of this distributions and their values

g) write the distribution mathematically and write the possible values the random variable can take on

h) in mathematical term, state what we are looking for (part a, b, c, d)

i) to find this probability by R, (part a, b, c, d) what is used and state the results. what does these results mean about the context of the question?

2. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.

a) Find the probability that at least four of the 25 patients actually have the flu.

b) On average, for every 25 patients calling in, how many do you expect to have the flu?

c) identify the random variable and what it represents/denotes

d) what distribution does the random variable follow and why? list the values this RV can take on and justify the choice of distribution

e) identify the parameters of this distribution and their values

f) write the distribution in mathematical terms and list possible values that the RV can take on

g) state what we are looking for in mathematical term (part a, b)

h) to find this probability by R, (part a, b) what is used? what is the result and what does this result mean about the context of the question?