Probability under Normal Curve
Z- Score of age = -1.18982.
Probability from normal curve: p (x < -1.19) = 0.1170
Z- Score of experience = -0.96937
Probability from normal curve: p (x < -0.97) = 0.1660
Z- Score of satisfaction = -0.66125
Probability from normal curve: p (x < -0.66) = 0.2546
Interpreting Z score
For age :
x = 26, μ = 41.0526, σ = 12.65119
= -1.18982
From the results above, the original z-score for age is equal to the given score.
For experience :
x = 2, μ = 12.2632, σ = 10.58742
= -0.96938
For experience, the original z-score is compatible with the given score.
For satisfaction :
x = 2, μ = 2.6316, σ = .95513
= -0.66127
From the results above, the original z-score for satisfaction is compatible with the given score.
Defending Conclusions
The three distributions above meet the criteria for normal distributions. This is because the mean, mode and median of the variables (age, experience and satisfaction) have very little deviations. Accurate z scores are important for comparing two scores from different normal distributions. Additionally, they help us predict the probability of a score occurring in a normal distribution.
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Summary of Findings
On the first section of the exercise above, the first Z- score was selected from each of the given variables. The probability of each score under the normal curve was then checked using the Z- tables. For age, the first Z- score was -1.18982, and the probability under the normal curve was 0.1170. For experience, the first Z- score value was -0.96937, and the probability from the normal curve was 0.1660. For satisfaction, the first Z- score was -0.66125, and the probability of this score from the normal curve was 0.2546.
For the second section of the exercise, the mean and standard deviation of the original variables were used to calculate Z- scores of the selected scores above. This was then compared with the given Z- score values to determine whether they are compatible. From the results, the calculated (original) z-score of age is equal to the given score. Similarly for experience, the original z-score is compatible with the given score. Lastly for satisfaction, the original z-score is compatible with the given score. Therefore, all the given Z- scores are compatible with the original Z- scores calculated using the mean and standard deviation of the original scores.
