# homework help

#### aharris05

##### New Member
Hi, I have been working on my assignment all day and came to this problem, I am not sure what to calculate to get the answers requested, any help would be appreciated..

The population of SAT scores forms a normal
distribution with a mean of = 500 and a standard
deviation of =100. If the average SAT score is
calculated for a sample of n = 25 students,

a. What is the probability that the sample mean will
be greater than M = 510? In symbols, what is
p(M = 510)?
b. What is the probability that the sample mean will
be greater than M = 520? In symbols, what is
p(M  520)?
c. What is the probability that the sample mean will
be between M =510 and M = 520? In symbols,
what is p(510
M
520)?

#### SPR

##### New Member
Hello Aharris05,

What is a sample mean?
What is a sample std?
What is a distribution of sample mean?
How to calculate sample z scores z1 for M=510 and z2 for M=520?
What is the probability of having z > z1, z > z2 and z1 < z < z2?

Sincerely,
SPR

#### aharris05

##### New Member
ok thank you for your help!

#### Mean Joe

##### TS Contributor
These questions pertain to the sample mean. The sample mean is a random variable; determine the mean and standard deviation of this r.v (you are given $$\mu$$, $$\sigma$$, and n).

Then you can calculate p(M>510), etc. in the usual way for normal random variables (yes, the sample mean in your problem is a normal r.v.)