00:01
The average price of a personal computer is 949, and they are normally distributed.
00:08
So let's draw our normal distribution.
00:12
The mean, 949, the standard deviation, 100.
00:19
Our first question is the probability, but a randomly selected pc costs between 950 and 1 ,100.
00:27
So let's mark those two cutoff points on here.
00:30
950 is just above the mean, 1 ,100 quite far above the mean.
00:35
And we want everything that falls between these two values.
00:40
So how do we work better? well, in a normal distribution, you don't dive in with the raw data, you convert it into an az score.
00:50
Z is equal to x minus mu over sigma.
00:54
It tells you how many standard deviations away from the mean a value is.
00:59
So it standardizes it.
01:02
So we'll get our two z scores here.
01:07
1 ,100 and 950.
01:12
950 is 950 minus 949 divided by 100, just 0 .01.
01:17
1 ,100 minus 949 divided by 100 is 1 .51.
01:22
2 .949 divided by 100 is 1 .51.
01:25
There we go.
01:27
So how do we get the interval from these z scores? well, if you go to a z score table, for example, it gives you the area between your value and the mean.
01:37
So if i put in 0 .01, it will give me this tiny sliver here, which i'll do in red.
01:44
There it is.
01:45
If i put in 1 .51, it will give me this entire red plus green area.
01:51
And so if i have the red plus green area and i subtract the red area, i will be left with the green area.
01:58
And that area under this curve will correspond to the probability...