Answer to Question #118669 in Statistics and Probability for Michael

Question

Assume that the sustained wind speed of a hurricane is normally distributed. If it is known that a hurricane is going to touch down also a category 4 or 5 hurricane , we can say , based on the past data that there is a 16% chance that the hurricane will sustain winds of over 273km/h.

How many standard deviation above the mean is a hurricane that actually does sustain winds of 273 km/h?
What might the mean and standard deviation be for all hurricane classified as 4 or 5

Answer 1

there is a 16% chance that the hurricane will sustain winds of over 273km/h.  According to the 68% rule - (100-68)/2=16%, so it is exactly one standard deviation above the mean

Category 4 and 5 Hurricanes might  have an average of 257 km/h and a standard deviation of 16 km/h