Define random variable X as the annual rainfall in Chicago, which is a valuable metric for the local agriculture industry. From climatologically data, we can assume X has a normal distribution with mean 37 inches and a standard deviation of 7.5 inches.
i. Determine the probability the rainfall in a given year is between 26.8 and 47.2 inches.
ii. Find the value d that ensures X falls within the range 37 i d with a probability of 0.99.
iii. A farmer is deciding on whether to plot a new crop that will only be profitable if the next decade has significant rainfall. Determine the probability that at least 8 out of the next 10 years will have annual rainfall amounts greater than 40.2 inches, which is the expected requirement for the success of the new crop. Should the farmer plant the new crop?
