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Answer :
To find the numerical limits for a B grade from normally distributed test scores with a mean of 66.9 and a standard deviation of 7.9, we determine the z-scores that correspond to the 86th percentile (upper limit) and the 65th percentile (lower limit), and convert these z-scores to actual test scores.
The student is asking about finding numerical limits for a B grade in a normally distributed set of test scores with given mean and standard deviation. To find the numerical limits for a B grade, we need to determine the z-scores that correspond to the cumulative percentages for top 14% and bottom 65%, since a B grade lies between these two percentages. Since scores are normally distributed with a mean ( extbf{average score}) of 66.9 and a standard deviation of 7.9, we can use a standard normal distribution table or calculator to find these z-scores and then convert them into actual test scores.
First, we look at the standard normal distribution for the score that marks the top 14%, which will be the upper limit for a B grade. Since the top 14% is the same as saying 100% - 14% = 86%, we look for the z-score that corresponds to the 86th percentile. Similarly, the lower limit for a B grade corresponds to the top 35%, since the bottom 65% is excluded from a B grade, meaning we look for the 65th percentile.
After finding the z-scores, we would apply the following formula: actual score = (z-score * standard deviation) + mean. This will give us the numerical limits for a B grade. We round the scores to the nearest whole number if necessary, as per the student's instructions.
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