Question

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495495 and standard deviation 118118 . You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to 118100=1.18118100=1.18 . 118100√=11.8118100=11.8 . 118100⎯⎯⎯⎯⎯⎯√=1.09118100=1.09 . 118118 .

Answer 1

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be

`s = (\sigma)/(√(n)) \\\\s = (118)/(√(100)) \\\\s = 11.8`

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Explanation:

From the given information,

The population mean SAT critical reading score is

`\mu = 495`

The population standard deviation is

`\sigma = 118`

You choose an SRS of 100 students and average their SAT Critical Reading score.

`n = 100`

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean SAT critical reading score.

`\bar{x} = \mu = 495`

The standard deviation of the sample would be

`s = (\sigma)/(√(n)) \\\\s = (118)/(√(100)) \\\\s = 11.8`

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8