<p>A large number of random samples of size $n$ are taken from a normal population with mean $30$ and variance $36$ and the sample means are calculated. If at most $95$% of the sample means exceed $27$, find the largest possible value of $n$.</p>

A large number of random samples of size $n$ are taken from a normal population with mean $30$ and variance $36$ and the sample means are calculated. If at most $95$% of the sample means exceed $27$, find the largest possible value of $n$.

Using GC to find the possible value of n

Using GC to find the possible value of n

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