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PERT weights the most likely estimate four times against the optimistic and pessimistic extremes, producing a beta-distributed expected value. The standard deviation is the range divided by six, which lets you quote a confidence interval rather than a single misleading number.
PERT expected value
Expected = (Optimistic + 4 x Most likely + Pessimistic) / 6
Standard deviation
SD = (Pessimistic - Optimistic) / 6
Because the beta distribution PERT assumes is unimodal with most probability mass around the mode. The 1-4-1 weighting approximates its mean.
Because a normal distribution spans roughly six standard deviations, so the optimistic-to-pessimistic range is treated as that full span.