Answer:
The confidence interval at at 99% level of confidence is <em>93.7 ≤ μ ≤ 96.9</em>.<em> </em>
Step-by-step explanation:
Step 1:
We must first determine the z-value at a confidence level of 99%.
Therefore,
99% = 100%(1 - 0.01)
Thus,
α = 0.01
Therefore, the z-value will be
z_(α/2) = z_(0.01/2) = z_0.005 = 2.58
(The z-value is read-off from the z table from the standard normal probabilities.)
Step 2:
We can now write the confidence interval:
X - z_(α/2) [s/√(n)] ≤ μ ≤ X + z_(α/2) [s/√(n)]
95.3 - 2.58(6.5/√(104)) ≤ μ ≤ 95.3 + 2.58(6.5/√(104))
<em>93.7 ≤ μ ≤ 96.9</em>
Therefore, confidence interval is <em>93.7 ≤ μ ≤ 96.9 </em>which means that we are 99% confident that the true mean population lies is at least 93.7 and at most 96.9.
