Question

A standardized test for graduate school admission has a mean score of 151 with a standard deviation of 10 and a unimodal, symmetric distribution of scores A test preparation organization teaches small classes of 9 students at a time. A larger organization teaches classes of 64 at a time. Both organizations publis the mean scores of all their classes. Complete parts a through c below. a) What would you expect the sampling distribution of mean class scores to be for each organization? OA. The distributions cannot be determined, since the Central Limit Theorem does not apply. OB. The distribution for the larger organization will be approximately Normal with a mean of 151. The sample size for the smaller organization is too small for the Central Limit Theorem to apply O C. Both distributions will be approximately Normal with a mean of 151. O D. The distribution for the smaller organization will be approximately Normal with a mean of 151. The sample size for the larger organization is too large for the Central Limit Theorem to apply b) If either organization has a graduating class with a mean score of 161, they'll take out a full-page ad in the local school paper to advertise. Which organization is more likely to have that success? Explain SD above the mean for the larger organization. It is more likely that A mean score of 161 is SD above the mean for the smaller organization, and the organization will have that success (Rou al places as needed Click larger inswer(s) smaller

Answer 1

If the population is distributed as with mean =$\mu$ and variance =$\sigma^2$  

Then the mean of sample of size n from this population have  sampling distribution with mean = $\mu$ and var =$\sigma^2/n$

So, the larger organization should have sampling distribution of mean = 151 and sd = $10/\sqrt 9 =3.33$

and the smaller organization should have sampling distribution of mean =151 and sd =$10/\sqrt {64} =1.25$

a) Option c . Both distribution will have a mean of 151

b) A mean score of 161 is 3 sd above the mean of smaller organization and 8 sd above the larger organization .

So, The smaller organization is more likely .

c)

A mean score of 161 is 1.5 sd below the mean of smaller organization and 4 sd below the larger organization .

So, The smaller organization is more likely .