SOLUTION: The average length of a phone call Jack and Jill receive is 3.6 minutes with a standard deviation of 2.1 minutes. a) Find the probability that any particular call will last betw

Algebra ->  Probability-and-statistics -> SOLUTION: The average length of a phone call Jack and Jill receive is 3.6 minutes with a standard deviation of 2.1 minutes. a) Find the probability that any particular call will last betw      Log On


   

Question 1088600: The average length of a phone call Jack and Jill receive is 3.6 minutes with a standard deviation of 2.1 minutes.
a) Find the probability that any particular call will last between 2 minutes and 5 minutes.
For this question I got 0.524 (I think that's right)
I'm struggling with b, I think I use normal Distribution but I'm not sure what to do after that, like how to use.
b) Jack and Jill each receive a phone call at the same time. (There are two lines into the office).Find the probability that at least one lasts longer than 4 minutes.
Thank-you for your help! Honestly! Thanks so much for spending your time to help :)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) Yes, correct.
.
.
.
b) Look at the possible outcomes:
1:Jack<4, Jill<4
2:Jack<4, Jill>4
3:Jack>4, Jill<4
4:Jack>4, Jill>4
The probability of each outcome would be,
P%281%29=P%28z%29%2AP%28z%29
P%282%29=P%28z%29%2A%281-P%28z%29%29
P%283%29=%281-P%28z%29%29%2AP%28z%29
P%284%29=%281-P%28z%29%29%281-P%28z%29%29
Find the z score using 4 minutes,
z=%284-3.6%29%2F2.1
So then the probability you want is,
P=P%282%29%2BP%283%29%2BP%284%29
P=2%2AP%28z%29%281-P%28z%29%29%2B%281-P%28z%29%29%5E2
P=1-P%28z%29%5E2