Question

Suppose you record how long it takes you to get to school over many months and discover that the one-way travel times (including time to find parking and walk to your classroom), in minutes, are approximately normally distributed with a mean of 23.88 minutes and standard deviation of 5 minutes.

A)If your first class starts at 10am and you leave at 9:40am, what is the probability that you will be late for class?

B)You choose your departure time in such a way that there is a 5% chance of arriving late for class. What is your departure time?

Answer 1

This is a normal distribution question with

A) P(x > 20.0)=?
The z-score at x = 20.0 is,

z = -0.776
This implies that
P(x > 20.0) = P(z > -0.776) = 1 - 0.2189
P(x > 20.0) = 0.7811
B) First we find what are the top 5% travel times

Given in the question
P(X < x) = 0.95
This implies that
P(Z < 1.645) = 0.95
With the help of formula for z, we can say that

x = 32.1

So we should depart at 9:27.9 am
PS: you have to refer z score table to find the final probabilities.
Please hit thumps up if the answer helped you