Thread: 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

Originally Posted by zkm1223

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

b) Calculate Pr(X - 2Y > 0) where U = X - 2Y is a random variable. Somewhere in your class notes or textbok (or just use Google) you will find the theory that allows you to write down its pdf ....

c) The mean of a sample is a random variable. Somewhere in your class notes or textbok (or just use Google) you will find what its pdf is when the sample is chosen from a normal population ....

If you need more help, please show all your work and say where you get stuck.