use r code please

i .A study on breeding birds collects information such as the length of their eggs (in mm). Assume that the length is normally distributed with mean = 43.5mm and standard deviation = 4.35mm. Assuming the appropriate probability distribution

a. What is the probability of finding an egg with a length greater than 50 mm? Give your answer correct to two decimal places.

b. What is the probability of finding an egg between 28 and 39 mm in length? Give your answer correct to two decimal places.

c. What is the 80th percentile value for egg length in mm? Give your answer correct to the nearest mm.

ii. A fisherman catches, on average, 4 fish in an hour. Let Y be a random variable denoting the number of fish caught in one hour and let X be the time interval between catching two fish. We assume that X follows an exponential distribution and that Y follows a Poisson distribution

a. What is the E(Y)?

b. What is the E(X) in minutes? Give your answer correct to the nearest minute.

c. What is the probability that the fisherman catches 5 or more fish in an hour? Give your answer correct to two decimal places.