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. (1 point) 65.4 and 90.6 59.1 and 96.9 71.7 and 84.3 69.7 and 86.3

Explanation:

Step1: Recall the formula for usual values

Usual values are within \( \mu\pm2\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.

Step2: Calculate the minimum value

The minimum value is \( \mu - 2\sigma \). Substitute \( \mu = 78 \) and \( \sigma=6.3 \): \( 78-2\times6.3=78 - 12.6=65.4 \).

Step3: Calculate the maximum value

The maximum value is \( \mu + 2\sigma \). Substitute \( \mu = 78 \) and \( \sigma = 6.3 \): \( 78+2\times6.3=78 + 12.6=90.6 \).

Answer:

65.4 and 90.6