What we are looking for is the confidence interval.
Given:
Sample it is denoted by n = 10
Mean = 80
Standard deviation = 12
Confidence Interval = 99%
Now compute for the margin of error, the formula is Za/2 * σ/√(n)
A 99% level of confidence has a critical value of zα/2 = 2.58.
The standard error is σ/√(n) = 3.162
Multiply 2.58 by 3.162 = 9.8 is the margin of error.
The formula for confidence interval is x̅ ± Za/2 * σ/√(n)
= 80 ± 9.8
= 70.2 < x< 89.8
