Question

Suppose commute times in a large city are normally distributed and that 66.60% of commuters in this city take more than 20 minutes to commute one-way. If the standard deviation of such commutes is 6.4 minutes, what is the mean commute?

Answer 1

Given that,

mean = = 20

standard deviation = =6.4

Using standard normal table,

P(Z > z) = 60.60%

= 1 - P(Z < z) = 0.6060

= P(Z < z ) = 1 - 0.6060

= P(Z < z ) = 0.394

= P(Z < z ) = 0.394

z = -0.27 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= -0.27 *6.4+20

x= 18.27