The total snowfall per year in Laytonville is normally distributed with mean 99 inches and standard deviation 14 inches. Based on the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 127 inches? Enter your answer as a percent rounded to 2 decimal places
According to Empirical rule, 68%, 95% and 99.7% of data lies within 1, 2 and 3 standard deviations of mean respectively.
Mean = 99 inches
Standard deviation = 14 inches
(127 - 99)/14 = 2
127 is 2 standard deviation from mean
95% of data is within the interval 99 2x14 =
(71, 127)
remaining 5% is either below 71 or above 127. 2.5% below 71 and 2.5% below 127
Therefore, probability that in a randomly selected year, the snowfall was less than 127 inches = 95 + 2.5
= 97.5%
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