How to use Weibull distribution when it comes to wind?

[Kolika28]

Homework Statement

I'm asked to find out how many hours of the year that the wind is between 4,5 m/s and 5,5 m/s.

Relevant Equations

Weibull formula

I know that I'm supposed to use Weibull, but why does my teacher take the middle value, 5 m/s? Should one not integrate the formula and the use 4,5 and 5,5 as limits? This is what he has done:

He then writes: makes a guess of an interval of 1 m/s and get:

To be honest, I really don't understand how to use Weibull distribution, and it would be great if someone could explain. I tried finding some websites, but I don't understand. How do I find the probability for one specific wind speed, or find the probability for an interval like this problem I posted?

 

[haruspex]

I don't think you need to integrate the given pdf, just use the CDF https://en.m.wikipedia.org/wiki/Weibull_distribution#Cumulative_distribution_function
Using the midpoint of the pdf is ok if you have some reason to suppose it is roughly linear in that range.

 

[Kolika28]

Thank you so much!