Well without making any assumptions, the only thing I can think of is that 4 out of the 9 observations are between 0.18 and 0.21.
4/9
The problem states:
Given the following soil water content data and making no distributional assumptions, what is the probability that the next sample will have a soil water content between 0.18 and 0.21?
0.28 0.15 0.25 0.17 0.23 0.18 0.21 0.18 0.19
So far, I've figured out the mean (0.204) and variance (0.0018) of the data. If I could assume a distribution I would use the appropriate CDF to figure out prob(X<0.21) - prob(X<0.18), but I can't assume a distribution....or standardize and use a table because, again, the whole assumption thing. I feel like I'm missing something really obvious and will give it a good "doh!" once someone puts it out there. Someone wanna help bring on that forehead smack?
Thanks for your help!!!
Well without making any assumptions, the only thing I can think of is that 4 out of the 9 observations are between 0.18 and 0.21.
4/9
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