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.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

about 168 miles

step-by-step explanation: