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.