Assume the scores of the students are normally distributed if not explicitly stated and report answers by rounding to two decimal places. When looking at the z table, round the values to two decimal places and consider the closest one.

For example, if the area under the curve is 0.79. In the z table, 0.78814 corresponds to z value of 0.80and 0.79103 corresponds to 0.81. Please consider 0.78814 from the z table as 0.78814 rounded to two decimal places = 0.79.

Report your answers rounded to two decimal places wherever it is applicable.

1. Suppose the scores of the class in exam 1 is normally distributed with median score of 85 and variance of 25. What is the percentage of students scoring outside two standard deviations of the mode score? (1 point)

2. In the above question, what is the percentage of students scoring less than 75? (1 point)

3. Find the interval (not the z scores but the actual scores) that covers 60% of the students on both sides of the mean (1 point)

4. Suppose the mean score of the class is 90 and the scores of the students are normally distributed. P(X>85) = 0.25. What is wrong in this question? (0.5 points)

5. Suppose the mean score of the class is 75 and the scores of the students are normally distributed. P(X>80) = 0.24. Calculate the standard deviation of the scores of the students. (0.5 points)

6. Henry scored 90^th percentile in the exam and Adam scored 50^th percentile in the exam. The scores of the students are normally distributed. How many standard deviation is Henry score away from Adam score. (Please mention explicitly the sign whether + or - as well) (1 point)