00:01
This problem says a researcher is again interested in the height, weight, and tv watching habits of 10 year old children.
00:05
Suppose that the weights of all 10 year olds in the us are normally distributed with a mean of 70 and a standard deviation of 10.
00:11
The researcher randomly selects a sample of size 16 from this population of 10 year olds.
00:15
Use this information to answer questions a through c.
00:18
And first for a, we want to define the sampling distribution of the mean in terms of its mean, standard deviation, and shape.
00:24
And the mean of our sampling distribution of the mean is going to be equal to the mean of the population, which is 70.
00:30
But the standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population, divided by the square root of the sample size, n.
00:38
So in our case that's 10 divided by the square root of 16, which gives us 10 over 4, which would then simplify to 5 halves, or give us 2 .5 as our standard deviation of the sampling distribution of the mean.
00:50
And our shape, since we were told that the population was distributed normally, we can say that our sample is also approximately normally distributed.
01:00
And now for parts b and c, we are looking at the probability first would be that the, of obtaining a random sample of size 16 with a sample mean of 73 or higher.
01:10
So since we can treat this like a normal distribution, since the population was normal, we can use normal cdf in our calculator to figure this probability out...