![]() To answer this question we first have to know what a normal distribution is. If the lecturer wishes to assign A grades to the best 15%, what is the cut-off Z-score and the corresponding cut-off raw score for A grade? Students’ examination scores for elementary statistics was found to be normally distributed with an average (mean) score μ of 50 and a standard deviation σ of 10. So what do we have here? The calculation says that (although the raw score of 85 for biology is greater than the raw score of 70 for chemistry) the corresponding Z-score for chemistry is greater than the Z-score for biology which implies that actually the student has better results for chemistry than for biology with respect to the class average.įor biology, the student scored 1.5 standard deviations above the average and for chemistry, the student scored 2.0 standard deviations above the average.Ī negative Z-score would indeed mean that the student scored below the average. The proportion of students who scored between 68 and 73 points is: P(68 Look for the value 0.75 in the positive z-table: 0.77337.Look for the value -0.5 in the negative z-table: 0.30854.Still following the same example (□ = 70 and □ = 4), what proportion of students scored between 68 and 73 points? At this point, we've obtained the proportion of students who scored less than 64 points (P(Z Since the z-score is negative, look for the value -1.5 in the negative z-table: 0.06681 (or 6.681%).Compute the z-score: □ = (64 - 70) / 4 = -1.5 (this result means that a score of 64 points is 1.5 standard deviations below the mean).Since the z-score is positive, look for the value 1.25 in the positive z-table: 0.89435 (89.435% of the students scored less than 75 points).įollowing the previous example (□ = 70 and □ = 4), what proportion of students scored more than 64 points?.Compute the z-score: □ = (75 - 70) / 4 = 1.25 (this result means that a score of 75 points is 1.25 standard deviations above from the mean).What is the z-score of the value 75? In other words, what proportion of students scored less than 75 points? ![]() Suppose the scores on a college exam are normally distributed with a mean □ of 70 and a standard deviation □ of 4. The intersection between the column and the row corresponds to the p-value. ![]()
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