Prediction error in a random sample

[Charlotte87]

I have an exercise that I do not understand how to solve (statistics and probability is really my weaker part...). The exercise goes as follow:

In a certain population, the random variable Y has variance equal to 490. Two independent random samples, each of size 20, are drawn. The first sample is used as the predictor of the second sample mean.

a) Calculate the expectation, expected square end variance of the prediction error.
b) Approximate the probability that the prediction error is less than 14 in absolute value.

any clues how I can start?

 

[Simon Bridge]

You need to look at how sample means are distributed.

 

[Charlotte87]

But how do I know how it is distributed? There is no information about that in the exercise.

 

[Simon Bridge]

The information is presented in your course notes - the part where it talks about how to combine two samples perhaps? You will also see that the variance calculation is different for a sample than for a population.

The distribution of the means of successive samples is related to the distribution of the population.