Question

A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of the trip-length to be normally distributed. During a period of 20 work days, on how many days should you expect the lawyer to be late for work?

Answer 1

Answer:

lawyer will be late for at least 17 days

Explanation:

given,

average time for a one way trip = 24 minutes

standard deviation = 3.8 minute

$Z = \dfrac{x-\mu}{\sigma}$

P(of late) = P(x>20 min)

 = $P(Z>\dfrac{20-24}{3.8}) = P(z>-1.05)$

= 0.5 + 0.3531

= 0.8531 = 85.31 %                    

days lawyer would be late for work

 = n p = 20 × 0.8531 = 17.062 days

hence, lawyer will be late for at least 17 days during a period of 20 work day.