00:02
I've drawn us a normal distribution here centered at 1252 with a standard deviation of 129.
00:09
And now we're going to figure out the probability of a bag of chips having less than 1 ,225 chips in it.
00:19
So to calculate that, we're going to need to calculate our z score, which will be our observed value 1225 minus the mean divided by the standard deviation.
00:35
That's going to give us a z score of negative .21.
00:46
So then we're going to reference the standard normal probability table in the back of the book and look up a z score of negative 0 .21, which is 0 .168.
01:05
So the chance of getting a bag of chips with less than 1 ,225 chips is 0 .4168 or 41 .68%.
01:14
And then, of course, for more than 1225, we're going to do 1 minus 0 .4168, which will give us a probability of 0 .3532.
01:32
Now, our next question, we want the percentile rank for a bag of chips with 150 chips in it.
01:41
So essentially what we want here is the probability of getting a bag of chips with less than 150 chips.
01:49
Chips.
01:51
So we'll do our z score again, 150 minus the mean divided by the standard deviation.
01:59
And in this case, we're going to get a value of negative 1 .57.
02:09
And then looking that z score up in the back of the book gives us a probability of 0 .0582...