Hi I just need a quick help on the question below which I ran into some difficulty while attempting.
A simple random sample of size n=18 is taken from a population with mean 16 and variance 5. the population distribution is assumed to be Normal. Let X be the mean of the sample. Answer the following questions.
(a) What is the distribution of X?
(b) What is P( X < 17 )?
(c) Suppose you need to choose a sample of size n such that
P( |X-16| > 1.5 ) < 0.05. What is the minimum n required to achieve this?
For (a) X = mean of sample. I took X~N ( 16, 5/18) = N (16, 0.278)
As for (b) I took P(X < 17) = P[ Z < (17-18)/Square root of 0.278 ]
= P ( Z < - 1.8966 )
Now, for part (b), I am not really sure how to continue. Should I minus the answer with 1? I am quite confused with the sign '<' and '>'
And for part (c), I am not really sure how to continue with an absolute value. Please help!