Question

An engineer commutes daily from her suburban home to her midtown office. The average time for a one­way trip is 32 minutes, with a standard deviation of 4.1 minutes. Assume the distribution of trip times to be normally distributed.

a) What is the probability that a trip will take at least 35 minutes?

b) Find the probability that exactly 4 of the next 5 trips will take at least 35 minutes.

Answer 1

a) P(X > 35) = P((X - mean)/sd > (35 - mean)/sd)

                    = P(Z > (35 - 32)/4.1)

                    = P(Z > 0.73)

                     = 1 - P(Z < 0.73)

                     = 1 - 0.7673

                     = 0.2327

b) n = 5

p = 0.2327

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X = 4) = 5C4 * (0.2327)^4 * (1 - 0.2327)^1

              = 0.0112