central limit theorem..
The Central Limit Theorem - ~ N(0,1)
Where x is the observed value (in your case 23.5), x(bar) is the sample mean, and s is the sample standard deviation.
You want is P(Z<23.5), but first you need to standardize it using the CLT I mentioned above to get:
and then you would just use the normal table to obtain your percentage of how many student's sample mean is less than 23.5 (that's how I interpreted what the question was asking)
Sorry about that, made a mistake.
I copied this from - Central limit theorem - Wikipedia, the free encyclopedia
Let X1, X2, X3, …, Xn be a sequence of n independent and identically distributed random variables each having finite values of expectation µ and variance σ2 > 0. The central limit theorem states that as the sample size n increases the distribution of the sample average of these random variables approaches the normal distribution with a mean µ and variance σ2/n irrespective of the shape of the common distribution of the individual terms Xi.
and Zn converges in distribution to N(0,1)
Each Xi is the mean of Student i
Sn is the sum of the Student's means
X bar is the average of their averages
and n = 180
Now you need to find P(Z<Zn)