Uniform distribution question

#1
Large random samples of size n are taken from a population which follows a uniform distribution with mean 25 and variance of 22.
a) What is the expected value of the sample mean?
b) Can the Central Limit Theorem be applied in this case?
c) The probability that a sample mean is greater than 27 is 0.1587. Find n.
d) If the population followed a Chi-Squared distribution, how would you approach part c) of this question?

Is the expected value equal to the population mean? I guess I can use the central limit theorem, because the sample is 'large'. I have no idea how to tackle c), I probably need to somehow standardize it, but I dont know how. No clue about d) either. Help would be appreciated, thanks a lot.
 

Dragan

Super Moderator
#2
Large random samples of size n are taken from a population which follows a uniform distribution with mean 25 and variance of 22.
a) What is the expected value of the sample mean?
b) Can the Central Limit Theorem be applied in this case?
c) The probability that a sample mean is greater than 27 is 0.1587. Find n.
d) If the population followed a Chi-Squared distribution, how would you approach part c) of this question?

Is the expected value equal to the population mean? I guess I can use the central limit theorem, because the sample is 'large'. I have no idea how to tackle c), I probably need to somehow standardize it, but I dont know how. No clue about d) either. Help would be appreciated, thanks a lot.

In terms of part (c) it looks like one equation with one unknown...i.e.

\(Z=\frac{\bar{X}-\mu }{\sqrt{\frac{\sigma ^{2}}{n}}}\)

where the value of Z that is associated with p=0.1587 is Z = 1.

You should be able to do the rest.
 
#3
Thanks. I got n=5.5 and I don't think it makes sense.
1=(27-25)/((22/n)^1/2)
(22/n)^1/2=2
22/n=4
4n=22
n=5.5

Where did I get it wrong?
What about a) and b), am I right?