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

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

65.4 and 90.6

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

Answer 2

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 * 6.3`

`78-12.6`

`65.4`

The maximum usual test score is:

`Mean + 2 Standard-deviation`

`78+2 * 6.3`

`78+12.6`

`90.6`

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

65.4 and 90.6