show all formulas and all work - all work is by hand (may use a calculator) and show two decimal places for answers that require calculations

(CAN YOU PLEASE SHOW THE WORK BY HAND PLEASE

1. Describe the characteristics of the normal curve.

2. SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100. We can treat these values as population values, m = 500 and s = 100. Use these values to solve the following problems:

(a) For a student with a math SAT-Math score of 590, convert their SAT score to a z score.

(b) What percentage of students would have a SAT-Math score greater than 590?

(c) What percent of students would be expected to have a SAT-Math score between 450 and 550?

(d) What is the probability of having a SAT-Math score less than 540?