1. For a distribution of scores, X = 40 corresponds to a z-score of z = +1.00, and X = 28 corresponds to a z-score of z = -0.50. What are the values

What are the values for the mean and standard deviation for the distribution?  (Hint: Sketch a distribution and locate each of the z‑score positions.)

3. For a normal distribution,

          a.  What z-score separates the highest 10% from the rest of the scores?

          b.  What z-score separates the highest 30% from the rest of the scores?

          c.  What z-score separates the lowest 40% from the rest of the scores?

          d.  What z-score separates the lowest 20% from the rest of the scores?

4. A population consists of the following N = 10 scores: 0, 6, 4, 3, 12, 6, 7, 5, 1, 11

Your task is to enter the data for this variable into SPSS, use the descriptives command to do a z-transformation of the whole distribution into a standardized distribution, and then get the frequencies with mean and standard deviation for both the original raw scores distribution and the standardized distribution. Attach the printout with the frequencies to this homework.

Step 1: Open SPSS, go into SPSS Data Editor, enter the ten scores in the first column in the Data View Mode, name this variable “esteem” [in the Variable View Mode; click on left bottom buttons to interchange between both], and save the datafile under the name “esteem-sav” [via the menu File > Save]

Step 2: Do a z-transformation of all the scores for variable “esteem” [use either the DESCRIPTIVES command in the syntax window, or do it via menu Analyze > Descriptive Statistics > Descriptives]. Save the standardized variable with a new name, namely “zesteem”, in the same datafile.

Step 3: Get the frequencies with mean and standard deviation the two variables (“esteem”, “zesteem”) via the menu Analyze > Descriptive Statistics > Frequencies], and print out the results. Attach this printout to your homework. You can also do this with the FREQUENCIES command in the syntax window.