The sampling distribution of the mean of a sample of 20 members of a normally distributed population with a mean of 35 and standard deviation of 2.8 can be described as follows:
The sampling distribution is also normally distributed, with a mean equal to the population mean (35) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (2.8/√20 = 1.4).
This means that the distribution of the sample means will be centered around the population mean (35) and will have a standard deviation of 1.4.
It's important to note that the sample distribution will be approximately normal for samples of size 20 or larger, provided that the population distribution is normal. If the population distribution is not normal, the sample distribution may not be normal, even for large samples.
In summary, the sampling distribution of the mean of a sample of 20 members of a normally distributed population with a mean of 35 and standard deviation of 2.8 is normally distributed with a mean of 35 and a standard deviation of 1.4.