00:01
Hey there, welcome to numerate.
00:03
We have an owner of a fish market looking to see the weights of a catfish that are normally distributed, so we've given a mean of 3 .2 and a standard deviation of 0 .8.
00:13
If we have sample size of 4 fish, what is the percentage that the sample means are between 3 to 4 pounds? so let's first write what we're given here.
00:23
We give me a mean of around 3 .2 pounds, and we give a population standard deviation.
00:32
Of around 0 .8 pounds, 3 .2, 0 .8, and we have a sample size also given as 4 fish.
00:41
Now, with this, we're looking for the probability that the mean is between 3 and 4 pounds.
00:50
In order to find this probability, we have to split this probability into two parts.
00:55
The probability that the mean is less than 3 and the probability that the mean is less than 4.
01:06
In order to find each of these probabilities here, we have to set up a z -score equation.
01:13
So we have z equals our 3 -d value minus our mean of 3 .2 divided by, let's make higher, 3 minus 3 .2, divided by 0 .8, divided by the square root of our sample size 4.
01:39
We're going to compute this, and this will simply be, let's see here, 3 minus 3 .3.
01:47
2 divided by 0 .8 divided by 2 of negative 0 .5.
01:54
Now we can use the z score to find our probability by using a calculator or a table.
02:01
So we have the e -score negative 0 .5 and this will bring this to a probability of around 0 .30854.
02:14
Perfect.
02:15
Now let's do the probability that the mean is less than 4.
02:18
We set up with z score equation again...