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Homework must be stapled, legible, and handed in before the beginning of lecture on the date indicated above. If you fail to turn in a homework, or turn it in late, you will receive zero points. Show all of your work, including the symbolic versions of any formulas that you use to derive your answers, round all intermediate and final results out to exactly 2 decimal places, and draw a box around your final answer.

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1) [5 pts.] For the following data calculate the range, the inter-quartile range, and mean absolute deviation. (we did the MAD in class for the case of a population, so do that on the homework).

5 3 9 2 0 1 4

2) (5 pts.) Find the variance and the standard deviation. Treat the data as a sample. New data: 5 3 9 2 0 1 3

3) [1 pt.] If the mean of a population (x) is 6, and the standard deviation is 8, then a raw score (i.e., a value of x) of 4 would correspond to a z score of what value?

NOTE: To receive full credit for each of the following problems (3-8), you’ll need to draw a picture of the distribution, indicating the critical areas. As always, read each problem CAREFULLY. Make sure that you understand exactly what is being asked.

4) [3 pts.]

a) What z score has 2.5% of the normal distribution below it?

b) What proportion of the normal curve is above a z score of 1.3?

c) What proportion of the normal curve is between the mean and a z score of 1.3?

5) [5 pts.] A student scores 91 on the midterm exam for Psych 60. Assume the class scores are normally distributed, with a mean (µ) of 65 and standard deviation (σ) of 15. The student’s exam score corresponds to what percentile?

For problems 6-9, use the following information:

In a class on Advanced Water Buffalo Husbandry, the midterm exam raw scores (i.e., the values of x) form a normal distribution, with a mean of 239 and a standard deviation of 37.

6) [5 pts.] What percentage of exam scores are more than 1.5 standard deviations of distance away from the mean?

7) [5 pts.] What proportion of students had an exam score between 180 and 250?

8) [5 pts.] 20% of the students had an exam score that was higher than what value?

9) [5 pts.] Which exam score corresponds to the 67th percentile?

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