The mean of the sampling distribution of mean sleep duration time for college students is 8.13.
The sampling distribution of the mean is a probability distribution that shows all possible sample means that can be obtained from a population. When we take a sample of size n from a population, calculate the mean of that sample, and repeat this process many times, we obtain a sampling distribution of the mean. The mean of this distribution is called the expected value of the sample mean, and it represents the average value of all possible sample means.
In this question, the population mean and standard deviation of sleep duration among college students are given as 8.13 and 1.87, respectively. We are asked to find the mean of the sampling distribution of the mean for a simple random sample of size 64.
The mean of the sampling distribution of the mean is equal to the population mean, which is 8.13 in this case. This means that if we take many simple random samples of size 64 from this population, calculate the mean of each sample, and plot these means on a histogram, the distribution of these means will be centered around 8.13.
The mean of the sampling distribution of the mean sleep duration time for college students can be calculated using the formula:
Sampling distribution mean = Population mean = 8.13
Therefore, the mean of the sampling distribution of mean sleep duration time for college students is 8.13.
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