Question

The scores of individual students on the american college testing (act) program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. at northside high, 36 seniors take the test. if the scores at this school have the same distribution as national scores, what is the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students?

Answer 1

Answer: The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students= 1

Explanation:

The standard deviation of the sampling distribution of mean is given by :-

`\sigma_x=(\sigma)/(√(n))`

, where
`\sigma` = population standard deviation.

n= sample size.

Given : The scores of individual students on the american college testing (act) program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. at north-side high.

i.e.
`\mu=18.6\ \ \sigma=6.0`

Sample size : n= 36

Then, the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students will be :-

`\sigma_x=(6)/(√(36))=(6)/(6)=1`

Hence, The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students= 1

Answer 2

The sampling distribution standard deviation is the population standard deviation divided by the root of the sample size.

sampling distribution standard deviation = 6.00/√36 = 1.00