For a continuous random variable x, the population mean and the population standard deviation are 80 and 15 respectively. You extract a sample of 25 elements from this population. The mean of the sampling distribution of the sample mean is
To find the mean of the sampling distribution of the sample mean, we can use the fact that the sampling distribution of the sample mean is normally distributed with a mean equal to the population mean (µ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n).
In this case, the population mean (µ) is 80, and the population standard deviation (σ) is 15. The sample size (n) is 25.
Therefore, the mean of the sampling distribution of the sample mean can be calculated as follows:
Mean of sampling distribution = µ = 80.
So, the mean of the sampling distribution of the sample mean is 80.