00:01
So we know for the first year, these salaries are supposed to end up having a normal distribution with a mean of 100 ,000 and a standard deviation of 15 ,000.
00:16
And then that they will also get a bonus.
00:20
And they said that bonus is normal with a mean of 25 ,000 and a standard deviation of 4 ,500.
00:27
And they said that these are independent.
00:30
So on part a, we need to find what the mean is for their compensation.
00:36
And let's just c is their compensation for the first year.
00:39
And that's to take their first year salary, which i'll call x, and their bonus that i'll call b, and add the two together.
00:48
So the mean for those, the mean of c would equal the mean of the first distribution, which is 100 ,000, plus the mean of b, which is 25 ,000.
01:01
So the average would be or the expected value, the expected value of that compensation for the first year would end up being 125 ,000.
01:13
Now what will the standard deviation be? so the standard deviation, and these are both for the first year, and the standard deviation of c is we have to add the variances.
01:26
And so we need to take the variance of the first group, which is that 15 ,000 squared plus 4 ,500 squared.
01:38
And then the sum of these two variances would be the variance of the compensation, and we want the standard deviations.
01:45
So from the calculator on, square root of 15 ,000 squared plus 4 ,500 squared.
01:53
And we find that that comes out to be $15 ,660 .46.
02:02
That's the standard deviation.
02:05
Now, on part c, we're dealing with the second year.
02:09
And the second year, the salaries are supposed to increase 15%.
02:15
Well, the increase in salary will also be an increase in standard deviation...