14. Let\'s say that I give you an exam with 40 questions. Your raw score corresp

Question

14. Let's say that I give you an exam with 40 questions. Your raw score corresponds to the number ofquestions you got correct. If I curve the exam, I want the mean to be 70% (which corresponds to a C), and I want the standard deviation to be equal to 10% so that the average distance from the mean for each person is 10%. Convert each of the raw scores to z-scores then to the new raw scores in the new standardize distribution (with a mean of 70 and a standard deviation of 10). Assume this is a population. X (number of questions correct) Standardized score (in a distribution with a mean of 70 and standard deviation of 10) z-score 35 30 15 30 bn o/ 40 *Hint: to find the z-score, you'll need to calculate the mean and standard deviation for the original raw scores first.

Explanation / Answer

X X- (X-)^2 z = X - / 35 5 25 0.598 30 0 0 0.000 15 -15 225 -1.793 30 0 0 0.000 40 10 100 1.195 total 150 350 mean() 150/5 30 variance 350/5 70 std deviation () square root of variance 8.37 Std X = standardised score standardised mean = = 70 standardised std deviation = = 10 X z score Std X = (z*) + 35 0.598 75.976 30 0.000 70.000 15 -1.793 52.072 30 0.000 70.000 40 1.195 81.952

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