97th percentile

#1
"suppose the moisture content per pound of a dehydrated protein concentrate is normally distributed with a mean of 3.5 and standard deviation of 0.5. A random sample of 16 specimens each consisting I a one pound concentrate is to be tested. Letting x bar denote the sample mean of these measurements of moisture content:
....find the 97th percentile of x bar.

I am a little confused...do I look up 0.9700 in the body of the table an then use x = u + (z•standard deviation)?
So it would be x = 3.5 + (1.88•0.5)?

I got the others correct I believe..
One stated find the probability that x bar will exceed 3.7
I did 3.7-3.5/0.125=1.6 checked the table and got 0.9452 then 1-0.9452=0.0548

But this percentile one is confusing me...

Any help?
 

Dason

Ambassador to the humans
#2
That isn't quite right since you're taking a sample of 16. Is the standard deviation of the mean for a sample of size 16 the same as the standard deviation of the population? (Hint: The answer is no).