This chart accurately shows the probability density functions for
three normal distributions.
I estimate that the probability that a variable drawn from the blue
distribution is negative is $0.25$. Can you suggest how I made this
estimate? Is it likely to be an over- or under-estimate?
How about the probabilities that random variables drawn from the
other distributions are negative?
My friend says that the means and variances of these normal
distributions are whole numbers. Can you use your estimates to work
out the values for these means and variances, using just tables and
estimates? Can you specify the values exactly, or can you only
specify a certain range of possibilities?