SOLUTION: i am not exactly sure what im doing here. Do i need a program to take 1000 sample means or is there anyway i can solve this by hand. thank you Suppose the number of

Question 234297: i am not exactly sure what im doing here. Do i need a program to take 1000 sample means or is there anyway i can solve this by hand.
thank you

Suppose the number of points scored in basketball games played by a particular college is normally distributed with mean  = 68 and standard deviation  = 12. A random sample of
9 games played by this team are taken.
(a) Name the sampling distribution of . Is it exact or approximate?
(b) What are the mean and standard deviation of ?
(c) What is the probability that:
(i) will exceed 72?
(ii) will fall below 65?
(iii) will lie between 68 and 71?
(iv) will be exactly equal to 70?
(d) Find a numerical value that is larger than 97.5% of all sample means.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose the number of points scored in basketball games played by a particular college is normally distributed with mean  = 68 and standard deviation  = 12. A random sample of
9 games played by this team are taken.
(a) Name the sampling distribution of the sample means. Is it exact or approximate?
The distribution of the sample means approches a Normal distribution
-----------
(b) What are the mean and standard deviation of ?
The mean of the sample means is 68 ;
The std of the sample means is 12/sqrt(9) = 4
--------------------------
(c) What is the probability that the mean of a sample of size 9:
(i) will exceed 72?
t(72) = (72-68)/4 = 1
P(t>1 with df=8) = 0.1733
-------------------------------
(ii) will fall below 65?
t(65) = (65-68)/4 = -3/4
P(t<-3/4 with df=8) = 0.2374
---------------------------------------
(iii) will lie between 68 and 71?
t(68) = 0
t(71)=(71-68)/4 = 3/4
P(68 < x < 71) = P(0 < t < 3/4,with df=8) = 0.2626
---------------------------------------
(iv) will be exactly equal to 70?
P(t = 70) = 0
Note: In a continuous distribution, the probability
that t = "any particular number" is always zero.
====================================================
(d) Find a numerical value that is larger than 97.5% of all sample means.
Use the form x = zs+u and solve for "x".
The z-value that has 97.5% of the population above it is
invT(0.975,8) = 2.306
So x = 2.306*4+68 = 77.2240
That is the sample mean value that is larger than 97.5% of
all the sample means of samples of size 9 when the population
has mean 68 and a standard deviation of 12.
===============================================
Cheers,
Stan H.
==================================
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