Assignment

1. For a distribution of scores, X = 40 corresponds to a zscore of z = +1.00, and X = 28 corresponds to a zscore of z = -0.50. What are the values for the mean and standard deviation for the distribution? (Hint: Sketch a distribution and locate each of the zscore positions.) Solution: we know Z=(x-µ)/𝞼  then we get x=µ+𝞼Z…..(1) For X=40 and Z=1 we get from (1) ,  40=µ+𝞼…………(2) For X=28 and Z=-0.50 we get from (1), 28=µ-0.50*𝞼…………(3) Subtracting (3) from (2)  we get 40-28=µ+𝞼- µ+0.50*𝞼=1.50𝞼 ð  12=1.50𝞼 ð  𝞼=8. ð  Putting 𝞼=8 in equation (2) we get µ=40-8=32 ð  Hence the mean µ=32 and standard deviation 𝞼=8 3. For a normal distribution,           a.  What z-score separates the highest 10% from the rest of the scores? Solution:Z-scores separates the highest 10% from the rest of the scores is 1.282           b.  What z-score separates the highest 30% from the rest of the scores? Solution: Z-scores separates the highest 30% from the rest of the scores is 0.5244.           c.  What z-score separates the lowest 40% from the rest of the scores? Solution: Z-scores separates the highest 40% from the rest of the scores is -0.253           d.  What z-score separates the lowest 20% from the rest of the scores? Solution: Z-scores separates the highest 20% from the rest of the scores is -0.8416 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. Statistics esteem Zscore(esteem) N Valid 10 10 Missing 0 0 Mean 5.5000 .0000000 Std. Error of Mean 1.22247 .31622777 Median 5.5000 .0000000 Mode 6.00 .12934 Std. Deviation 3.86580 1.00000000 Variance 14.944 1.000 Skewness .404 .404 Std. Error of Skewness .687 .687 Kurtosis -.357 -.357 Std. Error of Kurtosis 1.334 1.334 Range 12.00 3.10414 Minimum .00 -1.42273 Maximum 12.00 1.68141 Sum 55.00 .00000 esteem Frequency Percent Valid Percent Cumulative Percent Valid .00 1 10.0 10.0 10.0 1.00 1 10.0 10.0 20.0 3.00 1 10.0 10.0 30.0 4.00 1 10.0 10.0 40.0 5.00 1 10.0 10.0 50.0 6.00 2 20.0 20.0 70.0 7.00 1 10.0 10.0 80.0 11.00 1 10.0 10.0 90.0 12.00 1 10.0 10.0 100.0 Total 10 100.0 100.0 Zscore(esteem) Frequency Percent Valid Percent Cumulative Percent Valid -1.42273 1 10.0 10.0 10.0 -1.16405 1 10.0 10.0 20.0 -.64670 1 10.0 10.0 30.0 -.38802 1 10.0 10.0 40.0 -.12934 1 10.0 10.0 50.0 .12934 2 20.0 20.0 70.0 .38802 1 10.0 10.0 80.0 1.42273 1 10.0 10.0 90.0 1.68141 1 10.0 10.0 100.0 Total 10 100.0 100.0     For any kind of stats related problem please contact.We are here for easy and quick solution.