00:01
There is a normal distribution in this question and it is given that the mean is given.
00:08
So let me just take this values note.
00:11
So the mean which is denoted by me, that is 5 million.
00:18
This is 5 million.
00:22
And what about the standard deviation? the standard deviation, which is denoted by sigma, which is 1 ,7 ,750 ,000.
00:37
On let's say since this is a normal distribution i can define the random variable x which is normally distributed it has 5 million mean value in the standard division 1 million 750 ,000 great so in part a what we have to do let me just graph the normal distribution first but the question is being asked what is the probable that the profit on the job exits 8 million dollars so we need to find the random variable x which is greater than this is 8 million so we have to just find this probability here so what that means if i just graph the normal distribution here here is the mean value and the 8 million is over here so we have to just find the area of this region in order to get this area we have to use the normal cdf function of the ti calculator for the shaded region, the lower boundary is 8 million.
01:43
And the upper boundary, there is no upper boundary.
01:46
That goes to infinity.
01:47
So i'm going to put a very big number here.
01:50
And the mean value is 5 million.
01:55
And the standard division, 1 ,750 ,000.
01:59
Great.
02:00
Let's get the answer.
02:01
In order to get normal cdf, just press second.
02:04
In distribution, there is normal cdf here.
02:07
The lower boundary is 8 million.
02:12
The upper boundary is 1.
02:14
This is in 99.
02:17
And the mean value is 5 million.
02:24
And the standard division, 1 ,750 ,000.
02:29
Great.
02:30
Let's press enter and we got the probability here, which is 0 .04 and 32.
02:38
This is the answer for part a.
02:41
And the next part of the question, it says, what is the probability that the development make a loss? that means the profit is less than zero.
02:51
So we just defined random variable x, which is less than zero.
02:58
So we have to get this one here.
02:59
So the zero is, let's say, this is over here, and we have to just get the area of this region here.
03:07
And what we have to do, again, we're going to use the normal.
03:11
Cdf function.
03:15
So when this case, the lower boundary, that goes to negative in the so i'm going to put a very small number here.
03:21
The upper boundary is zero.
03:23
The mean value is 5 million and 1 ,750 ,000...