Normal Distribution Help Please

Hi, in my homework, I am stuck on a three part question. I have managed to do the first part of the question but can't understand how to do the second and third part of the question. Please can somebody help.

Here is the question:

The journey to or from work has a mean of 67 minutes and a standard deviation of 15 minutes. You can assume a normal distribution of journey times.

a) What's the probability the workers total traveling time to and from work is more than 151 minutes? (My Answer: 28.43%)

b) If John and Jack are selected at random from an office, what is the probability that John takes more than twice as long as Jack to get home?

c) What is the probability that the average journey time of 10 random people is at least 65 minutes?

Thanks

(edited 13 years ago)

Reply 1

ghostwalker

Original post by zkm1223

...

You're basically looking at linear combinatons of normally distributed (presumably independent) random variables; the theory should be in your textbook, or is easy enough to Google.

I've not checked part a/

b) If John's time is denoted by N, and Jack's by K; have a think how you would combine them to get what the question is asking.

c) Think about how you work out an average/mean, and use that to find the distribution of the mean. Call the distrubtion of your ten people X1, X2, etc.

Reply 2

zkm1223

Still don't understand what you mean and how to work it out

Reply 3

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

Original post by zkm1223

Still don't understand what you mean and how to work it out

Do these look familiar
E(aX+bY)=aE(X)+bE(Y)
Var(aX+bY)=a^2Var(X)+b^2Var(Y)
?

Reply 4

zkm1223

I don't recall seeing these formulae

Reply 5

ghostwalker

Original post by zkm1223

I don't recall seeing these formulae

In that case you're missing a chunk of teaching. You need those results for part a) as well. I'd suggest looking in your textbook or searhing online for "linear sum normally distributed random variables" or some combination like that.

Reply 6

John taylor

Can someone help me with this normal distribution question.

The random variable x - N (symbol Mu, sigma squared)
The lower quartile of X is 25 and the upper quartile of X is 45.
Find the value of Mu and the value sigma.

Please show your working
Thank you :smile:

(edited 13 years ago)

Reply 7

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

Original post by John taylor

Please show your working.

Noone should post an answer for you. You need to show us what you can do and where you're stuck.

Reply 8

John taylor

Original post by Get me off the £\?%!^@ computer

Please show your working.

Noone should post an answer for you. You need to show us what you can do and where you're stuck.

I don't know how to create the two probabilities eqautions with the unknowns.

Reply 9

Rational Paradox

Original post by John taylor

I don't know how to create the two probabilities eqautions with the unknowns.

How much probability is contained by the LQ, and how much is contained by the UQ?

from there, you should be able to make an equation.

(edited 13 years ago)

Reply 10

John taylor

Hey, I was just wondering if i did this normal distribution question correctly because i dont have the answers!

Given that;
Mean = 27 and the variance = 10
Find P(26 < X < 28)

I did...
P (26-27 < z < 28-27)
____ ____
s.r 10 s.r 10
* note s.r means square root of 10
so i got P(-0.32 < Z < 0.32) * values to (2 decimal places)
....more working
and i ended up with an answer of 0.251
Is that correct?

Thanks :smile:

Reply 11

John taylor

* Note the square root of 10 is meant to be under (26-27) and (28 -27)!

Reply 12

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

Original post by John taylor

That's correct.

Try here next time. http://www.analyzemath.com/statistics/normal_calculator.html (second one on the page)

Don't expect the answers to agree perfectly. Working from tables using 2 d.p. won't give you as accurate an answer.