The average amount of snow per season in Trafford is 40 inches. The standard deviation is 4 inches. Find the probability that next year Trafford will receive the given amount of snowfall. Assume the random variable is normally distributed. Refer to the table of values (Area Under the Standard Normal Distribution) as needed. If necessary, round intermediate calculations to the nearest hundredth. Part 1 of 2 Your Answer is correct (a)At most 46 inches of snow The probability that Trafford will receive at most 46 inches of snow is 93.3% . Part: 1 / 2 1 of 2 Parts Complete Part 2 of 2 (b)At least 47 inches of snow The probability that Trafford will receive at least 47 inches of snow is % .
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 average amount of snow per season in Trafford is
Refer to the table of values (Area Under the Standard Normal Distribution) as needed. If necessary, round intermediate calculations to the nearest hundredth.
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The probability that Trafford will receive at least
47
%
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