I need help about 2 problems. It is about sampling distribution.
Assume the octane rating for a particular type of gasoline is normally distributed ramdom variable with a mean=87.0 and standard deviation=1.5.
-What is the probability the mean of a random sample mean of 5 measurements of the octane rating for this type of gasoline will be between 86.5 and 87.5?
Here I wanted to use the central limit theorem but the sample is not large enough. So I don't kow how to do it.
Suppose the probability that a communication is a signal, X=1, is 0.9, and the probability that a communication is noise, X=0, is 0.1. A random sample of 3 communications is to be taken, the value X, 0, 1, recorded and mean(X) computed. Find the sampling distribution of mean(X).