00:01
So in this question we're told that the sales in the next year, let's call them x, are normally distributed with a mean of 2 .5 million and a standard deviation of 300 ,000, so that's 0 .3 million.
00:17
So first of all, what's the probability that the sales will exceed 3 million? well, what we can do is we can write that z is x minus 2 .5 million divided by 0 .3 million.
00:33
So the x is greater than 3 million is the probability that z is greater than 3 minus 2 .5 divided by 0 .3, which is 1 .6667.
00:48
So because we've got a greater than sign, we do 1 minus the cumulative function of 1 .6667, and the cumulative function we can look up in a table.
00:58
So when we look it up and subtract it away from 1, we get 0 .0478, four decimal places.
01:10
What is the probability that it will be within 150 ,000 of the expected level? well, the expected level is 2 .5 million, so the probability that it's within 150 ,000 of that, well, 150 ,000 is 0 .15 million.
01:35
So we're looking at the probability that x is between 2 .5 minus 0 .15, which is 2 .35, and 2 .5 plus 0 .15, which is 2 .65.
01:51
Well, we can write that in terms of z values just using the formula above.
01:57
So 2 .35 minus 2 .5 is minus 0 .15 divided by 0 .3 is minus a half.
02:07
And 2 .65, well, when we subtract off 2 .5, we have plus 0 .15.
02:13
So that's going to give us plus a half.
02:16
So that's phi of a half minus phi of minus a half, and we can look those up in tables.
02:24
So phi of a half and take away phi of minus a half...