# Could someone check my review question? Probability

• Feb 12th 2008, 07:18 PM
jwells1999
Could someone check my review question? Probability
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?

Z score of -1 is .3413
.5-.3413=.1587
The probability that the trip takes more than 20 minutes is .1587 or 15.87%.

B)What is the probability the trip takes less than 15 minutes?

Z score is .4772
5-.4772=.0228
The probability that the trip takes less than 15 minutes is .0228 or 2.28%.

C)What is the probability the trip takes between 30 and 35 minutes?

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%.

D)What is the probability the trip takes more than 40 minutes?

Z score of 3 is .4986
.5-.4986=.0014
The probability that the trip will take more than 40 minutes is .0014 or .14%.
• Feb 12th 2008, 08:41 PM
mr fantastic
Quote:

Originally Posted by jwells1999
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?

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?

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: (Yes)

C)What is the probability the trip takes between 30 and 35 minutes?

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: (Yes) 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?

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% .......

..
• Feb 12th 2008, 09:07 PM
jwells1999
Does this look right?
X=20, z=(20-25)/5=-1
Z score of -1 is .3413
.3413+.5=.8413
The probability that the trip takes more than 20 minutes is .8413 or 84.13%

Does this look right for the first part. This is really trippin me up. I dont know why. (Emo)
• Feb 12th 2008, 09:48 PM
mr fantastic
Quote:

Originally Posted by jwells1999
X=20, z=(20-25)/5=-1
Z score of -1 is .3413
.3413+.5=.8413
The probability that the trip takes more than 20 minutes is .8413 or 84.13% Mr F says: (Yes)

Does this look right for the first part. This is really trippin me up. I dont know why. (Emo)

I find drawing simple pictures and shading in the area(s) of the things I want helps.