00:01
So there are many different ways that we can solve part a, but what i'll do is i'll use a website called salt, which is quite handy because we have the ability to set our mean value as we desire.
00:15
So we have mean value of 9 .9 and a standard deviation of 0 .19, where we can note that quite usefully, we're also, we also have this translated into what the zed scores for the lower and upper bounds would be.
00:29
They're both plus or minus negative or plus or minus 0 .98.
00:34
And we have that the probability in between is 0 .67291.
00:39
So we have for a, the answer is 0 .67291.
00:45
Then for part b, i'll type this out, or at least partially, be approximately normal because of the fact that the population is normally distributed.
00:59
We have that it would have a mean value so the mean it would be equal to 9 .9 ounces the standard deviation is going to be equal to the population standard deviation 0 .19 divided by the square root of the sample size is 16 here so we get that the standard deviation is equal to 0 .0475 then for doing this now we're going to have to go over to a t distribution with 15 degrees of freedom.
01:36
And let's see here.
01:40
So actually, what i'm going to do is use this page for figuring out the zed scores that we want.
01:48
So we want probability for the sample mean is less than 9 .86.
01:55
So 9 .86.
01:58
So it's a z score of negative 0 .8241.
02:01
Then we can go over to our t distribution...