SOLUTION: John can take on three possible routes from his home to his oce in the morning. The percentage of days on routes A, B, and C to his oce were 45%, 30%, and 25%, respectively. The

Algebra ->  Probability-and-statistics -> SOLUTION: John can take on three possible routes from his home to his oce in the morning. The percentage of days on routes A, B, and C to his oce were 45%, 30%, and 25%, respectively. The       Log On


   

Question 1150692: John can take on three possible routes from his home to his oce in the
morning. The percentage of days on routes A, B, and C to his oce were 45%,
30%, and 25%, respectively. The travelling time on each of these routes is
normally distributed with mean and standard deviation given in the following
table:
Mean:
Route A 30 minutes
Route B 35 minutes
Route C 28 minutes
Standard Deviation
A . 10 minutes
B . 8 minutes
C . 12 minutes
John left his home at 8:28am and arrived at his oce before 9:00am. Calculate
the probability that he took Route B to work?
Answer by Glaviolette(140) About Me  (Show Source):
You can put this solution on YOUR website!
The travel time was less than 32 minutes. Use that as X in the z-score formula. Therefore, z = (32-35)/8 = -0.375 = -0.38. From a z-table, area less than -0.38 is 0.3520. Therefore, the probability that he took route B, is .3520.