Question

The scores of individual students on the ACT Exam are modeled as normally distributed with a mean of19.6 and a standard deviation of 5.0. At Voldemort High, 64 seniors take the test. Assume the individualscores at this school are modeled using the same distribution as national scores. What is the samplingdistribution of the sample average score for this random sample of 64 students

Answer 1

The sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation 0.625.

Explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 19.6 and a standard deviation of 5.0.

This means that
`\mu = 19.6, \sigma = 5`

What is the sampling distribution of the sample average score for this random sample of 64 students?

By the Central Limit Thoerem, the sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation
`s = (5)/(√(64)) = (5)/(8) = 0.625`