A major exam company retains the ACT scores for all test takers for the last year. The mean composite ACT score for last year was 21.0 with a standard deviation of 5.4.

a. If were to create a sampling distribution from this data with samples of 30 exams from the data, what would the shape, mean, and standard deviation of distribution be? Why?

b. Would the shape, mean, or standard deviation of the sampling distribution vary if our sample size increased to 100 exams? If so, which ones would vary and why?

(a) 0.9858 (b) 0.54

Step-by-step explanation:

μ = 21.0, σ = 5.4

a) The shape of the sampling distribution would be approximately normal, the mean of the smaple would be 21.0 and standard deviation of the sample would be 0.9859.

S.D = \frac{\sigma }{\sqrt{n}}

S.D = \frac{5.4 }{\sqrt{30}}

S.D = 0.9859

b) The shape of the sampling distribution would be approximately normal, the mean of the smaple would be 21.0 and standard deviation of the sample would be 0.54.

S.D = \frac{\sigma }{\sqrt{n}}

S.D = \frac{5.4 }{\sqrt{100}}

S.D = 0.54

The sample standard deviation would vary becuase as the sample size increases the sample S.D decreases.

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

d

step-by-step explanation: