00:01
It's stated here that the distribution of women's weights is normal with the mean of 135 pounds and a standard deviation of 21 pounds.
00:11
And for the first question we were asked for the probability that a randomly selected woman's weight is less than 144 pounds.
00:19
So this is the probability that x is less than 144.
00:23
If this graph represents the normal distribution for women's weights has a mean of 135, standard deviation of 21, 144 is somewhere over here, and the probability that x is less than 144 is equal to the area under the curve and to the left of 144.
00:46
So that's the area of this blue -shaded region.
00:50
Now we can solve this using software such as excel.
00:53
So if we go to excel, we would start a computation with an equal sign.
00:58
We want to use the normal distribution function for the first argument we enter 144, and we enter the mean, and the standard deviation, or the cumulative argument we enter true because we want the probability that x is anything less than 144, we hit enter, and we get a probability of .6659 approximately.
01:27
And then for the second question, we were asked for the mean of the sampling distribution of the means for samples of size 25.
01:35
So if we were to take samples of size 25, what is the mean of the distribution of sample means? so in other words, what is the mean of x bar? that is equal to the mean of the population, which is 135.
01:56
And then for the third question, we're asked for the standard deviation of the sampling distribution of sample means for samples of size 25...