00:01
We're looking at a normal distribution, so i will start by drawing it.
00:08
Total area under this curve is 1, or 100%, and it's symmetric.
00:12
Half of boards will be shorter than the mean, half longer than the mean.
00:17
The mean mu is 101, standard deviation sigma 0 .5.
00:24
For part a, we pick a board at random.
00:26
What is the probability its length is greater than 101 .22? that's above the mean, and we want greater than, so the area to the right.
00:39
You need something that will take you from area under the curve to a probability, or rather, a value to area under the curve, i .e.
00:49
Probability.
00:50
But the normal functions are really complicated.
00:53
We don't do this by hand.
00:55
You need something to do it for you.
00:57
That could be a z -score table, which would be fine for part a, but for part b would give you a less accurate answer, because it makes you round your z -score.
01:05
So i'm going to use technology.
01:06
It could be software, like excel or r.
01:09
It could be a graphical calculator.
01:10
I'm going to use a ti -84 calculator, with the normal cdf function.
01:18
Into this i need to put a lower bound, an upper bound, a mean, a standard deviation.
01:25
And it will give me the area between the lower and upper bounds.
01:28
So for part a, lower bound is of course 101 .22.
01:35
Upper bound really should be infinity.
01:38
The normal distribution is asymptotic to the x -axis...