For a random variable X with mean μ, variance σ², and cumulants κn, its quantile yp at order-of-quantile p can be estimated as
The values γ1 and γ2 are the random variable's skewness and (excess) kurtosis respectively.
We can use the first two bracketed terms above, which depend only on skew and kurtosis, to estimate quantiles of this random variable.
For the 95th percentile, the value for which the standard normal cumulative distribution function is 0.95 is 1.644854, which will be x.
For comparison, the 95th percentile of a normal random variable with mean 10 and variance 25 would be about 18.224; it makes sense that the normal random variable has a lower 95th percentile value, as the normal distribution has no skew or excess kurtosis, and so has a thinner tail than the random variable X.