Suppose that at Northside High, the number of hours per week that seniors spend on homework is approximately Normally distributed with a mean of 18.6 and a standard deviation of 6.0. We take a simple random sample of 36 seniors and calculate the sample mean homework hours per week. What is the mean of the sampling distribution of means for the 36 students

The mean of the sampling distribution of means for the 36 students is of 18.6 homework hours per week.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

In this question:

For the population, the mean is 18.6. So, by the Central Limit Theorem, the mean of the sampling distribution is also 18.6.