Draw a normal curve on the x-axis marking the middle point
as the mean 352.  Then mark off units right and left by adding the
standard deviation 20 to the mean to mark points to the right and 
subtracting 20 from the mean to get points on the left side. 



We'll draw a green "cut-off" line at 352: 

 

We want the area to the left of the green line above.  We can use the
z-distribution even with a sample size less than 30, because we are
assuming that we know sigma.  We also must assume that the distribution
is known to be normal, for if it is not we cannot do the problem at all with
that small a sample.  That's because the central limit theorem only holds for
sample sizes of 30 or more when the population is not known to be normally
distributed.  So your problem should have stated that the distribution
is known to be normal for otherwise, and for the problem to be doable,
you would need a sample size of 30 or more.  I will assume the population
is known to be normal.

Press ON
Press CLEAR
Press 2ND
Press VARS
Press 2

you should see  " normalcdf(  " with the flashing cursor after that) 
After that type 

-99999999,352,368,38/Ö(20))

That's a negative sign, (-), not a minus sign! 
The comma key is just above the 7 key.

You should see this on your screen:

normalcdf(-99999
999,352,368,38/Ö
(20))

Press ENTER   

you see .029849806

That's about .03 or 3%, so only 3% of the time
would a sample size be that low, so we would rightfully
suspect that the claim that the mean is 368 is incorrect.

Edwin