Question

An English professor determined the mean of her final exam scores to be 78 with a standard deviation of 6.3. Find the minimum and maximum “usual” values of the test scores.


65.4 and 90.6


69.7 and 86.3


71.7 and 84.3


59.1 and 96.9

Answer 1

Solution: We are given:

$Mean =78, Standard-deviation =6.3$

We know that a usual values of the test scores falls within 2 standard deviation from the mean.

Therefore, the minimum usual test score is:

$Mean - 2 Standard-deviation$

$78-2 \times 6.3$

$78-12.6$

$65.4$

The maximum usual test score is:

$Mean + 2 Standard-deviation$

$78+2 \times 6.3$

$78+12.6$

$90.6$

Therefore, the minimum and maximum “usual” values of the test scores are:

65.4 and 90.6

Answer 2

Answer:

The minimum and maximum usual value of the test scores are:

              65.4 and 90.6

Step-by-step explanation:

We know that:

The maximum usual value is two standard deviations above the mean and the minimum usual value is two standard deviation below the mean.

i.e.

Maximum value= Mean+2×standard deviation.

i.e.   Maximum value= 78+2×6.3

Maximum value= 90.6

and

Minimum value= Mean-2×standard deviation.

Minimum value= 78-2×6.3

i.e. Minimum value= 65.4