Question

a set of 1000 values has a normal distribution. The mean of the data is 120 and the standard deviation is 20

Answer 1

The sampling distribution of the sample mean would be approximately normally distributed, centered around the population mean. The standard deviation of the sampling distribution would be smaller than the standard deviation of the population. The standard error of the mean can be calculated as the population standard deviation divided by the square root of the sample size.

Step-by-step explanation:

The question is asking about what we would expect to see in the sampling distribution of the sample mean if we draw 100 samples of size 40 from a normally-distributed population with a mean of 50 and a standard deviation of four.

When we calculate the mean of each sample, we would expect the sampling distribution of the sample means to be approximately normally distributed, centered around the population mean of 50.

We would also expect the standard deviation of the sampling distribution of the sample means to be smaller than the standard deviation of the population, which is known as the standard error of the mean. In this case, the standard error of the mean would be the population standard deviation divided by the square root of the sample size, which is four divided by the square root of 40, or approximately 0.6325.

Answer 2

In order to find 90%, you need to look for 90% on a normal distribution curve, which has a z-score of 1.29.

The solution would be like this for this specific problem:

-120 / 20 = 1.27

You would require 145.4 and 90% lie under that point.