00:01
We're going to let x equal the number of particles in a sample.
00:11
And since it says it's 50 per millimeter, so per every one millimeter, i can do 50 times 5, and i'll have 250 particles per 5 millimeters.
00:28
I'm going to do a poison distribution where x is distributed and a poison distribution for 250 milliliters.
00:43
So my mean is 250, and my standard deviation will be square root 250.
00:55
I want to find the probability that x is between 235 and 265.
01:05
So i'll start by finding the z score for each of those values, where z is x minus mean over standard deviation.
01:27
So i'll end up with a probability that z is, is between negative 0 .95 and positive 95.
01:39
I can rewrite that as the probability that z is less than than 95 minus the probability that z is less than negative 0 .95.
01:51
That's going to allow us to use, excuse me, allow us to use our standard table.
01:57
Using the standard table, i'll find the values for z of 0 .82894 minus 0 .17106 and we'll get a probability of 0 .65788.
02:17
For part b, i want to look within a 5 milliliter sample.
02:25
What's the probability of x being between 48 and 52? so same as above, we're going to find our z value.
02:36
This time using the formula x minus mean over standard deviation divided by square root a sample size.
03:01
Solving for that, we're going to get the probability that z is between negative point 28 and positive point 28.
03:10
We can rewrite that as the probability that z is less than 0 .28 minus the probability that z is less than negative 0 .28.
03:22
Using our standard table, we can find those values as 0 .616 minus 0 .38974 for a probability of 0 .22052...