Tenorio National Park in Costa Rica has a roughly consistent year-round climate. On any given day, we assume there is a 40% chance of heavy rain.

a. We are interested in forecasting the number of heavy rain days during 2019. Write down n and p if we are to use the binomial distribution for this forecast.

b. Calculate the mean and standard deviation of heavy rain days in 2019 using the binomial model. Use R or a calculator.

c. Find the probability that the park will experience exactly 145 days of heavy rain in 2019.

d. Find the probability that the park will see between 125 and 175 days of heavy rain in 2019.

e. The yearly amount of rainfall in the park is normally distributed with mean 200 inches and standard deviation of 20 inches. Find the probability that the park will experience more than 230 inches of rain in 2019.