(a) The birth weights of babies are known to be normally distributed with a mean weight of 100

ounces and a standard deviation of 20 ounces. A "low birth weight" baby is one that is born in

the 6th percentile of this distribution. This is of concern for a variety of reasons, such as the fact

that low birth weight babies have lower rates of survival than normal birth weight babies.

i. Using the information above, what is the threshold weight for a low birth weight baby.

ii. Calculate the probability that the birth weight of babies;

A. are below 60 ounces.

B. above 150 ounces. {

C. between 100 and 140 ounces.

iii. Out of 10 babies born, what is the probability that exactly 1 of them will have 'very low birth

weight' (weights below 55 ounces).

iv. Out of 10 babies born, what is the probability that less than 2 of them will have 'very low

birth weight' (weights below 55 ounces).

(b) Given a binomial distribution for X with n = 120 and p = 0.45,

i. calculate P(X > 50) using exact distribution.

ii. calculate P(X > 50) using Normal approximation.

(c) Given a Poisson distribution for X with = 25, calculate P ( X < 15) using Normal approximation.

Please solve this using R studio(the software) and provide answers to 4 decimal spaces if the answers are not exact.