Question

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

Answer 1

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%