Question

1. Suppose that a statistics assignment is given which has a mean of 65 and a standard deviation of 12.
   1. If the teacher informs you that your score was at most 1.5 deviations away from the mean, then what interval(s) of scores does your grade fall within?
   2. What is the z-score for an assignment grade of 88?
   3. What is the assignment score that corresponds to a z-score of -2.1?
   4. What is the meaning of a z-score in general? That is, what does it measure?
   5. Which is better relative to the class statistics? An 80 on the assignment referenced above or an 80 on an assignment with a class average of 65 and a standard deviation of 8? Why?

Answer 1

Solution:

Given: a statistics assignment is given which has a mean of 65 and a standard deviation of 12.

Part a)

a  score was at most 1.5 deviations away from the mean.

Find interval(s) of scores in which a grade fall within this interval.

that is find:

Thus an interval(s) of scores in which a grade fall is :

Part b)

Find  the z-score for an assignment grade of 88

Part c)

Find the assignment score that corresponds to a z-score of -2.1.

Use following formula to find x value:

the assignment score that corresponds to a z-score of -2.1 is 39.8

Part d)

z score is the number of standard deviations above or below the mean.

It measures how many standard deviations a score lie above or below from mean.

Part e)  

Find z score for both scores:

An 80 on the assignment referenced above:

An 80 on an assignment with a class average of 65 and a standard deviation of 8

Since z score for an 80 on an assignment with a class average of 65 and a standard deviation of 8 is more than z score for an 80 on an assignment referenced above, an 80 on an assignment with a class average of 65 and a standard deviation of 8 is better relative to the class statistics.