Suppose that on a stress index scale, the population of US adults has a mean of 200 and a standard deviation of 27. Assume the distribution is approximately normal.

If a person scored 165, what is their standard score?

If a person scored 165, what is their estimated percentile rank?

What is the lowest score you can get and still be in the top 1%?

What is the highest score you can get and still be in the bottom 5%?

The estimated percentile rank is 84.13%. What is X?