Question

Christopher has collected data to find that the total snowfall per year in Laytonville has a normal distribution. What is the probability that in a randomly selected year, the snowfall was greater than 53 inches if the mean is 92 inches and the standard deviation is 13 inches? Use the empirical rule Provide the final answer as a percent rounded to two decimal places. __%

Answer 1

The empirical rule of standard deviation for normal distribution says that

Where mean = 92 inches and standard deviation is 13 inches hence No of standard deviation, 53 inches can be calculated as

92-3*13=53 , hence 53 inches is 3 standard deviation below the mean, so Probability for snowfall greater than 53 inches is the area above -3 standard deviation which is calculated from above given image as

P(X>53)= 0.9985 or 99.85 %