The lawyer will get coffee if he reaches office between 8.50AM to 9.00AM. This means between 20 minutes to 30 minutes after leaving home at 8.30AM. Consider the trip time as variable x. We have to calculate probability P( 20<x<30). The mean value of x is 24. Since the trip time is normally distributed about the mean, we can find the z-score for the end points ( a<z<b) as follows:

a == -1.05

and b =1.58

Thus P(20<x<30)= P(-1.05<z<1.58)

= (z curve area to the left of 1.58)- (z curve area to the left of -1.05)

= 0.9429- 0.1469

= 0.7960

This means that the probability that he gets coffee at office is 0.7960.

Hence the probability that he misses coffee at office is 1- 0.7960 = 0.2040

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