00:01
So here we're given that the average weight here, our mu value is 244 .8, with a standard deviation of 40, and we're told that we're taking a sample of size 35.
00:16
So when we consider the distribution of sample means, the mean value should be equal to the mean value of the population, and the standard deviation of the sample means is going to be equal to that of the population.
00:31
Divided by the square root of the sample size.
00:34
That's going to be 40 over root 35, which gives us a value of 6 .76, roughly.
00:45
Then, let's see here.
00:47
Okay, so that's actually already what we were asked to do.
00:51
I was just doing that as setup, but that's basically part a.
00:55
So we're asked, what is the probability that the sample mean will be less than 239 pounds? so the way that we can go about doing this is first convert 239 pounds into a z score, which we do by taking 239 minus the mean value of the sample means, divided by the standard deviation of the sample means, which gives us a standard, a z score here of negative 0 .8579, roughly.
01:29
Or actually that would round to 0 .8580 to four decimal places.
01:35
So that probability is going to be equal to the probability of a z score being less than negative 0 .850, which we can find using a table of values, something like that.
01:49
We should find that the result here is going to be 0 .19545 roughly.
01:56
Then let's see here probability of more than 239 pounds for the next part or pardon me more than 238 pounds so we'll have probability of x bar greater than 238 is equal to probability that a standard variable or a standard or a z score is greater than a value of negative 1 .006 roughly when we can convert 238 to a z score there, which then is going to be equal to 0 .8428, roughly.
02:40
And let's see here, we're looking then for probability that a sample mean is between 251 and 258...