Our equation is:

Confidence Interval = sample mean +/- critical value * (sample standard deviation / square root of n)

From the word problem we know:

Sample mean = 65.9

Sample standard deviation = 6.3

N (sample size) = 50

Critical value for 99% = 2.576

Our math should look as follows:

Confidence Interval = 65.9 +/- 2.576*(6.3 / sqrt of 50)

= 65.9 +/- 2.576*(6.3 / 7.07)

= 65.9 +/- 2.576*.891

= 65.9 +/- 2.295

= 65.9 - 2.295 = 63.605 or 63.6

= 65.9 + 2.295 = 68.195 or 68.2

So our answer is [63.6, 68.2] for the 99% confidence interval, so option A is the correct answer.