00:01
We're looking at a normal distribution.
00:03
I'll start by drawing it.
00:06
The total area under this curve is 1 or 100 % and it is symmetric.
00:10
Half of these ball bearings will have a diameter below the mean, half above the mean.
00:15
The mean, mu, is 3.
00:17
The standard deviation, sigma, is 0 .2.
00:21
Okay, they are rejected if their diameter is less than 2 .75, so that's below the mean, or greater than 3 .25.
00:31
So we'll mark those on here.
00:34
So if they fall into this shaded area or this one, they are rejected.
00:40
For part a, what are the z -scores of these rejected ball bearings? so a z -score tells you how many standard deviations away from the mean a value is.
00:50
You can calculate it by taking the value, subtracting the mean, and dividing the difference by the standard deviation.
00:57
Doing that here, we have 0 .25 over 0 .2, or minus 0 .25 over 0 .2.
01:03
These two cut off points giving us plus and minus 1 .25.
01:09
Both of these values are 1 .25 standard deviations away from the mean.
01:13
Positive means above the mean, negative means below the mean.
01:17
Part b, what percent of ball bearings will be rejected? so if i find these areas and find the total, that will tell me the proportion rejected, then i can turn that into a percentage.
01:29
But to find that, i need something with the normal distribution already built in, because the function i would have to integrate to get this area under the curve is too complicated for us to do by hand.
01:40
So you could use a z -score table, you have that here...