Normal Distribution: Raw scores

Suppose we have a population of scores with a mean(mu) of 200 and a standard deviation(sigma) of 10. Assume that the distribution is normal. Provide answers to the following questions:

1. What score would cut off the top 5 percent of scores?
2. What score would cut off the bottom 5 percent of scores?
3. What score would cut off the top 2.5 percent of scores?
4. What score would cut off the bottom 2.5 percent of scores?

Please see the attachment.

Z table questions
Suppose we have a population of scores with a mean (µ) of 200 and a standard deviation (σ) of 10. Assume that the distribution is normal. Provide answers to the following questions:
Answers
Let X be the score of the population. Given that X is normal with mean µ = 200 and standard deviation  = 10.
Standardizing the variable X using and from …

The solution provides step by step method for the calculation of raw scores using the Z score. Formula for the calculation and Interpretations of the results are also included.