00:01
John has two jobs for daytime work at a jewelry store.
00:03
He is paid $15 ,000 per month plus the commission.
00:06
His monthly commission is normally distributed with a mean of $10 ,000 and a standard deviation of $2 ,000.
00:15
John has a good job.
00:18
John's income levels from the two sources are independent of each other.
00:26
Use this information to answer the following questions.
00:29
For a given month, what's the probability that john's commission from the jewelry store is less than $13? $13 ,000.
00:35
It's a probability that x is less than $13 ,000.
00:40
It's the probability that z is less than $13 ,000 minus 10 ,000, divided by 2 ,000.
00:48
And that's the probability that z is less than 1 .5, which is 0 .9332.
00:56
For part b, for a given month, what's the probability that john's commissioned from the jewelry store is at least 12 ,000? it's a probability that x is greater than or equal.
01:05
To a 12 ,000 is 1 minus the probability that z is less than 12 ,000 minus 10 ,000 divided by 2 ,000.
01:15
So now our 1 minus probability that z is less than 1, which corresponds to 0 .1587.
01:24
Part c, for a given month, what's the probability john's commission from the jewelry store will be between 11 and 12 ,000? so 11 ,000 is going to be 0 .5.
01:44
We already know that 12 ,000 is 1 for a z score.
01:48
So we'll take 0 .8 -413 and subtract 0 .6915 for probability 0 .1498.
01:56
So a pretty low probability of making less than that $12 ,000, a pretty decent probability making more than $13 ,000 in commission.
02:07
So d.
02:10
The probability is 95 % that john's commission from the jewelry store is at least how much in a month.
02:16
So 0 .95 corresponds to a z score of 1 .645.
02:20
We'll take x bar equals 10 ,000.
02:23
That's the mu plus our standard deviation times our z score.
02:28
And when we do that, we're going to get 13 ,290.
02:34
For e, we're going to do the same process this time...