7) A random sample of 12 scores from an exam are given below (20 pts) Exam score
ID: 3043636 • Letter: 7
Question
7) A random sample of 12 scores from an exam are given below (20 pts) Exam score: 88, 56, 87, 78, 81, 83, 78, 94. 75, 82.87,90 a) Find sample mean and sample standard deviation of the above data. b) Determine the criteria for: Significantly low score: Significantly high score: c) Is the score 56 a significantly low score? c) Use the sample mean and sample deviation from the test score data above to calculate the z-score for score 94. Use the z-score to determine if score 94 is a significantly high score. d) Calculate the z-score and percentile of score 78. Which one (z-score or percentile) indicates a better position for score 78?Explanation / Answer
7a) Sample mean = Sum/n= 979/12= 81.583
stdandard deviation =9.77
b) Criterian for low marks is the lowest score of sample and criterian for highest score is higherst score of sample.
c) significantly lowest score is 56
Z= x-mu/sigma
= 56-81.583/9.77
= -25.583/9.77
=-2.62
standard normal probability of -2.62 is .0044 which isvery small and hence 56 scoreis significantly low score.
d) X= 94
Z= X-mu/Sigma
=94-81.583/9.77
=12.417/9.77
=1.27
Standard normal probability corresponding to this is 0.8980 which isvery high . So it issignificantly high score.
e) X= 78
Z= x-mu/sigma
= 78-81.583/9.77
= -3.583/9.77
= -0.3667
64% percentile.
Percentile indicates 78 score better.
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