The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.84 inches and a standard deviation of 4.34 inches. The annual precipitation amount has a normal distribution. (Give your answers correct to four decimal places.) (d) What is the probability that next year the total precipitation for New York State is more than 35.7 inches? (e) What is the probability that next year the total precipitation for New York State is less than 44.2 inches? (f) What is the probability that next year the total precipitation for New York State is less than 32 inches?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.84 inches and a standard deviation of 4.34 inches. The annual precipitation amount has a
(d) What is the
(e) What is the probability that next year the total precipitation for New York State is less than 44.2 inches?
(f) What is the probability that next year the total precipitation for New York State is less than 32 inches?
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