There is going to be a question like this on a test coming up and I just wanted to see if I was doing it right. Could somebody maybe check my answer for me? Thanks

p.s. If I did it wrong can you show me how to do it?

The time it takes to travel from home to the office is normally distributed with mean = 25 minutes and SD = 5 minutes.

A)What is the probability the trip takes more than 20 minutes?

my answer---X=20, z=(20-25)/5=-1

Z score of -1 is .3413

Mr F says: More than 20 minutes .....You want Pr(X > 20), which boils down to Pr(z > -1).
.5-.3413=.1587

Mr F says: This is Pr(z < -1). You want Pr(z > -1) ......
The probability that the trip takes more than 20 minutes is .1587 or 15.87%.

Mr F says: You should have ralised immediately that this answer is wrong. 20 is less than the mean. So how on Earth can Pr(X > 20) be LESS than 0.5??
B)What is the probability the trip takes less than 15 minutes?

my answer-X=15, z=(15-25)/5=-2

Z score is .4772

5-.4772=.0228

The probability that the trip takes less than 15 minutes is .0228 or 2.28%.

Mr F says:
C)What is the probability the trip takes between 30 and 35 minutes?

my answer-x=30, z=(30-25)/5=1

x=35, z=(35-25)/5=2

p(30<x<35)=P(1<z<2)

P(30<x<35)=(.3413<x<.4772)

.4772-.3413=.1359 or 13.59%

The probability that the trip takes between 30 and 35 minutes is .1359

Or 13.59%.

Mr F says: Although the setting out of your working leaves a bit to be desired ......
D)What is the probability the trip takes more than 40 minutes?

my answer-X=40, z=(40-25)/5=3

Z score of 3 is .4986

.5-.4986=.0014

The probability that the trip will take more than 40 minutes is .0014 or .14%.

Mr F says: I get 0.00134996722, which will round to 0.0013, correct to 4 decimal places. Or 0.13% .......