00:01
Okay, we have here then a normal distribution, which means the usual bell shape curve like this.
00:09
Here is x, the data value.
00:13
And this rule, 68, 95 and so on, what it means is if i start here at 70, with a mean in the middle, and i go one standard deviation either side.
00:26
In other words, i go up to 85 and down to 55.
00:33
So add on 15, take away 15.
00:36
This area here is going to be 68%.
00:39
In other words, here is 34 % and here is 34%.
00:45
Within 2sd of the mean, what happens? i get 95 % of the data.
00:51
So to add 15 again, that will be 85 plus 15 is 100.
00:57
55 take away 15 is going to be 40 and what means this entire area here is 95 % of the total so that means either side of that i take 95 and divided by 2 i get 47 .5 which means this must be 13 .5 this area here and here is 13 .5 so it makes the entire area 95 percent and the last one 99 .7 is three sd away from the mean it's not required here don't think that will be 115 way over here so you have over here 115 and down here would be 25 but that we don't need in this question now the first one says percentage below 40 so on a then percentage below 40 that will be this area here on my diagram well what i have so far is 34 and 13 .5 is 47 .5 take that from 50 half of the area and 2 .5 so this will be 2 .5 point let's get relaxed, shading first.
02:44
So this area here is 2 .5 because this old area here is 50%.
02:51
Half of the graph below 70.
02:58
2 .5%.
03:02
Now part b says between 40 and 85.
03:09
So 40 to 85...