Standard Deviation - Estimation

[Skelly4444]

We have wind speeds recorded during the month of June, of which the highest recorded was 17kn and the lowest 4kn.
I have calculated the mean wind speed as 8.1 and the standard deviation as 3.41 from the data given in the question and these are the values written in the back of the book and I understand them fully.

The question then says, estimate the number of days where the wind speed is greater than one standard deviation above the mean. The answer in the back of the book says 12 out of the 30 days and I cannot understand how they've obtained this value? Any pointers would be greatly appreciated.

Thanks
Simon

 

[Romsek]

In an actual normal distribution the probability of being 1 standard deviation above the mean or greater is roughly 16%.

16% of 30 is roughly 5 days.

I can't imagine where they obtained 12 from, unless your distribution isn't very normal and they just counted days from the data.

 

[Skelly4444]

It didn't mention that they are normally distributed, it just said that we are to assume that the wind speeds are equally distributed throughout the range. The lowest recorded value was 4kn and the highest was 17kn.

Is it possible to obtain 12 days as the answer with this in mind?

Thanks

 

[tkhunny]

"they are normally distributed"
"we are to assume that the wind speeds are equally distributed throughout the range"

Nope. Have to make up your mind.

What's the Empirical Rule for 1 standard deviation above the mean? Romsek already answered this.

16% is the expectation.
4.8 days is the Normal expectation
12 days may be a one-time realization.

 

[Dr.Peterson]

It didn't mention that they are normally distributed, it just said that we are to assume that the wind speeds are equally distributed throughout the range. The lowest recorded value was 4kn and the highest was 17kn.

Is it possible to obtain 12 days as the answer with this in mind?

Please quote the exact wording of the problem, including the data! As it is, we are guessing what you have to do.

As I understand it, it is NOT a normal distribution, but perhaps IS a uniform distribution. (No, that wouldn't give a mean of 8.1.) At any rate, it sounds like you have to just count the number of days in the data when the speed is greater than 8.1 + 3.41 = 11.51. Have you done that?