00:01
We are looking at a normal distribution.
00:02
I'll start by drawing it.
00:05
The total area under this curve is 1, or 100%, and it is symmetric.
00:10
Its mean is 30 seconds, with a standard deviation of 9 seconds.
00:15
In part a, we want to know the commercial length separating the longest 14 % from the rarest.
00:22
So that would be up here.
00:24
It's what we call the 86th percentile, defined as the point where 14 % is above it, so 0 .14, and the other 86 % below it.
00:36
To find this, you need something with the normal distribution built into it.
00:40
That could be software, like excel or r.
00:42
I'm going to use my ti -84 calculator, with the inverse normal function.
00:48
This has three inputs.
00:50
An area, a mean, a standard deviation.
00:52
It gives me the value on this particular normal curve, with area a to its left.
00:57
It's an inverse cumulative function.
01:00
I put in the cumulative area, 86%, with the mean and standard deviation.
01:06
The output is 39 .72 seconds.
01:13
That's the commercial length that separates the top 14 % from the bottom 86%.
01:18
Part b.
01:20
The probability of lasting between 33 and 49 seconds.
01:24
I have a different function for this.
01:26
Again, i'm using my ti -84, but you can find similar functions on any software you like.
01:31
Normal cdf.
01:33
It has four inputs.
01:34
Lower bound, upper bound, mean, standard deviation...