Scores on an assignment follow a normal model with mean of 75 and standard deviation on 10. Use the 68-95-99.7 rule to answer. PLEASE SHOW DETAILED WORKING, I have three questions and I want a format of the answers for this one.

Draw pictures.

What percentage of students score less than 55?

What percentage of students score greater than 95?

What percentage of students score between 65 and 85?

If a students gets a mark of 82, what is the z score of this mark? explain this z-score

BONUS: If a students gets a mark of 100, what is the z-score of this mark?

2. Heights of Math 2208 students follow a normal model N (165 cm, 15cm). What percent of students would you expect:

a)over 165cm?

b)under 160cm?

c) over 180cm?

d) more than + or - 1.35standard deviations away from the mean?

e) within + or - 1.35 standard deviations of the mean?