Question

A lawyer commutes daily from her suburban home to her midtown office, and she measures X=Time (min) to reach the office. Assume that the distribution of X is approximately Normally distributed with a mean time of 25 min and standard deviation of 4 min.

a.) what is the probability that her trip to work will take at least 30min?

b.) how long will the lawyers trip to work be such that 85% of her trips will take a longer amount of time?

c.) Suppose that one morning, the lawyer measures a trip time of 38 min. Would that be an unusual trip time for her? Explain

Answer 1

This is a normal distribution question with

a) x = 30
P(x > 30.0)=?

z = 1.25
This implies that
P(x > 30.0) = P(z > 1.25) = 0.1056
b) Given in the question
P(X < x) = 0.85
This implies that
P(Z < 1.036) = 0.85
With the help of formula for z, we can say that

x = 29.144
c) x = 38
P(x > 38.0)=?

z = 3.25
This implies that
P(x > 38.0) = P(z > 3.25) = 0.0006

Yes, unusual
PS: you have to refer z score table to find the final probabilities.
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