Question

the mean score on a statistics exam is 82. if your exam score is 2.12 standard deviations below the mean, which of the following scores could not be your exam score? (there may be multiple correct answers, click all that apply) group of answer choices a.70 b.85 c.80 d.90

Answer 1

The scores that could not be your exam score are a. 85 and d. 90.

Your exam score is 2.12 standard deviations below the mean of 82. This means your score is significantly lower than the average.

To calculate the possible range of your score, we can multiply the standard deviation (2.12) by 2 (since we're dealing with 2.12 standard deviations below the mean) and subtract that value from the mean. This gives us a lower bound of 70.56.

Similarly, adding 2.12 standard deviations to the mean gives us an upper bound of 93.44.

Therefore, any score below 70.56 or above 93.44 cannot be your exam score.

Option a (85) is above the lower bound and within the possible range, so it could be your score.

Option b (80) is also within the possible range, so it could be your score.

Option c (70) is below the lower bound and therefore cannot be your score.

Option d (90) is above the upper bound and therefore cannot be your score.

So, the correct answers are a. 85 and d. 90.

Answer 2

The scores which could not be the exam score are 85 and 90.

Using the parameters given for our Calculation ;

• Mean score = 82
• Standard deviation = 2.12

Values which are a given number of standard deviations 'below' the mean will be lesser than the mean value while those values which are a number of standard deviations 'above' the mean would be greater than the mean value.

Since, the score is a number of standard deviations 'below' the mean, then the test score cannot be greater than the mean.

Hence, 85 and 90 cannot be the test score.