Let the random variable X denote the annual snow fall amount at a well known Utah ski resort. X has a normal distribution with mean 500 inches and standard deviation 50 inches.
(a) What is the probability that in a given year the snow fall will be between 432 and 568 inches?
(b) Find a value d such that X is in the range 500 d with probability 0.999.
(c) What is the probability that at least 8 out of 10 consecutive years will have annual snowfall amount greater than 522 inches?