## log likelihood as measurement of distribution fit?

Hi, here's some information after fitting my measurements to a lognormal distribution. I assume the log logistics number is a measure of how well the distributions fits, is that correct?

What exactely does it mean that the log likelyhood is -67.175?? As of my understanding the log likelihood, is the natural logaritm of the likelihood function, which is the probability that these measurements comes from this distribution??

1. is that correct?
2. why is it negative?
3. How can i decide if this is a good distribution fit? (graphically it looks satisfying, im not in a need for extremely exact numbers for what im going to use them for)

from Matlab:
Distribution: Lognormal
Log likelihood: -67.175
Domain: 0 < y < Inf
Mean: 9.04552
Variance: 1.51012

Parameter Estimate Std. Err.
mu 2.19313 0.0208669
sigma 0.135233 0.0150259

Estimated covariance of parameter estimates:
mu sigma
mu 0.000435428 -2.49709e-018
sigma -2.49709e-018 0.000225778