A humanities professor sent a letter grade on a test according to the following scheme. A:...

A humanities professor sent a letter grade on a test according to the following scheme. A: top 12% scores. B: Score is below 12% and above the bottom 58%. C: score is below the top 42% and above the bottom 25% . D: scores below top 75% and above bottom 8% . F: bottom 8% of scores.

Scores on tests are normally distributed with a mean of 78.9 and a standard deviation of 9.3.Find the minimum score required for an average.

Solutions

Expert Solution

A: top 12% scores.
This represents students are 88 percentile and above

B: Score is below 12% and above the bottom 58%.

This represents student for are between 88 percentile and 58 percentile

We find the 58th percentile as follows

C: score is below the top 42% and above the bottom 25% .

This represents student for are between 58th percentile and 25th percentile

We find the 25th percentile as follows

D: scores below top 75% and above bottom 8% .

This represents student for are between 25th percentile and 8th percentile

We find the 8th percentile as follows

F: bottom 8% of scores.

This represents student for are between 8th percentile and 0th percentile

This grade system is shown below in the figure.

Therefore an average score would get a C grade.

orchestra answered 1 year ago

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