Question

central limit theorem: nationally, the composite score of students taking the act (american college testing) college entrance examination has a normal distribution with a mean of 18.0 and a standard deviation of 6.0. at kent roosevelt high school, 36 seniors take the test. assume the act scores at this school have the same distribution as national scores and the students who take the act test are considered as a simple random sample.a. Then the average ACT score of the sample of Kent Roosevelt students who took the test has a distribution function b. with mean c. and standard deviation (standard error)

Answer 1

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

What is standard deviation?

The standard deviation of the sampling distribution of mean is given by :- σₓ = σ/√n, where  = population standard deviation and n= sample size.

According to the given question:

The scores of individual students on the American college testing program composite college entrance examination have a normal distribution with mean 18.0 and standard deviation 6.0. at kent roosevelt high.

i.e. μ = 18.0, σ = 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 :-

σₓ = 6/√36 = 1

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

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