Distribution of test scores calculate cutoff given mean and standard deviation

Question

A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class?

Answer 1

Here is something to get you started: You need to find $a$ such that $P(X\leq a)=0.8$, where $X$ follows a normal distribution with a mean of 38 and standard deviation of 6. Now you need to standardize it. Remember that if $X\sim\mathcal{N}(\mu,\sigma)$ then $\dfrac{X-\mu}{\sigma}\sim\mathcal{N}(0,1)$.