I know that a distribution is a log normal with mean = 4744 and mode = 3777. I need to calculate the probability of X being lower than the mean.
In order to do so I need to calculate the CDF of my log normal distribution, and I know that I need to calculate the standard deviation to have the CDF. The problem is that I don't know how to get the standard deviation knowing the mean and the mode. I know what is the formulas of mean, standard deviation and mode, from these three I can substitute and reach the formula to get the standard deviation from the mode and the mean but I am not able to solve it.
I tried with simpy and this is the code, but when I try to run it python gets stucked:
x = symbols('x')
mode = 3777
mean = 4744
expr = mode -np.e**(mean - x)
sol = solve(expr)
Any idea or suggestions to solve this problem?