Justin is a grade 12 student planning to go to university next year. He has studied hard and is proud of his overall average of 82%. However, Justin is uncertain of where he stands in relation to other classmates applying to university. By using his understanding of statistics, Justin hopes to determine his chances of being accepted into the university of his choice.

Here is a list of the average marks of all the Grade 12 students in Justin's school who are applying to university.

75 72 76 63 64 66 70 82 76 72

53 48 81 77 64 79 71 75 78 72

78 67 63 90 87 77 75 70 59 75

76 78 55 74 71 73 69 85 63 54

1. Calculate the quartile values including the IQR.

2. In which quarter of the group does Justin's average mark of 82% fit?

3. Determine the standard deviation of the group of average marks.

4. Is this a normal distribution? If so, what range of marks makes up one standard deviation form the mean? Two? Three?

5. How many grade 12 students in Justin's school have an average mark within one standard deviation of the mean? Two? Three?

6. Is this consistent with the characteristics of a normal distribution?

7. Calculate a z-score for Justin's average mark.

8. What percentile is Justin in?

9. Using the z-score table, what percentage of students should have a lower average mark than Justin?

10. What would Justin's mark need to be if he wanted to be in the 90th percentile of his class?