Question

Suppose commute times in a large city are normally distributed and that 61.00% of commuters in this city take more than 21 minutes to commute one-way. If the standard deviation of such commutes is 6.4 minutes, what is the mean commute?

Answer 1

P(X > 21) = 0.61

Or, P((X - )/ > (21 - )/) = 0.61

Or, P(Z > (21 - )/6.4) = 0.61

Or, P(Z < (21 - )/6.4) = 0.39

Or, (21 - )/6.4 = -0.28

Or, = 21 + 6.4 * 0.28

Or,   = 22.792