My title might be a bit ambiguous so I will give full details under but I am not sure how to approach this question because I'm not even certain on what type it is.
Q: The height of students is normally distributed with mean 63.5 inches and standard deviation of 2.9 inches.
I need to find the smallest sample size n so that, with probability of at least 90 percent, at least one student in the sample is more than 72 inches tall.
What is the smallest value for n that fulfills this property?
Hint:
The z-score of the student is $\frac{72-63.5}{2.9}$ or $2.93$ (to $3$ s.f). Using a table or a GDC, the probability that a student has a $z$-score greater than $2.93$ is $0.00169$.
We can set the probability that no student is taller than $72$ inches using binomial probability to $0.1$:
$$0.1 = {n \choose 0} (0.00169)^0 (1 - 0.00169)^n$$
Now find $n$ and correct for the fact that you are using sample size.