Question at position 12 Scores on Dr. Bond's test have a mean of 70 and a standard deviation of 11. Michelle has a score of 48. Convert Michelle's score to a z-score. (Round to two decimal places if necessary.)41.641.33-22Clear my selection

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BlackTom AI · Accepted Answer

First, restating the problem: we are given a test with mean 70 and standard deviation 11, and Michelle scored 48. We need to convert this raw score to a z-score, rounding to two decimals if needed. 
Option by option analysis:
Option "41.64": This value suggests a very large positive z-score, which would occur if the raw score were much higher than the mean or if the standard deviation were negative. Neither is the case here, so this is incorrect. 
Option "1.33": This is a small positive z-score. Since Michelle’s score (48) is below the mean (70), a positive z-score would be inconsistent with the data; thus this cannot be correct. 
Option "-2": This option aligns with the standard z-score formula: z = (X − μ)/σ = (48 − 70)/11 = −22/11 = −2. It correctly reflects that Michelle’s score is below the mean by 22 points, measured in units of the standard deviation. Therefore this is the correct calculation. 
Option "2": This is a small positive z-score, which would imply Michelle scored above the mean, contrary to the given raw score of 48. Since 48 is less than the mean of 70, a positive z-score is inappropriate, so this option is incorrect. 
In summary, only the calculation producing −2 accurately represents how many standard deviations Michelle’s score lies from the mean, given the provided mean and standard deviation.}

Question at position 12 Scores on Dr. Bond's test have a mean of 70 and a standard deviation of 11. Michelle has a score of 48. Convert Michelle's score to a z-score. (Round to two decimal places if necessary.)41.641.33-22Clear my selection

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