Answer:
The 99% confidence interval for the weights = [71.36lb, 78.64lb]
Explanation:
Mean weight
[tex]\bar{x} =75 lb[/tex]
Variance of weights
[tex]\sigma^2 =100lb[/tex]
Standard deviation,
[tex]\sigma =\sqrt{100}=10lb[/tex]
Confidence interval is given by
[tex]\bar{x}-Z\times \frac{\sigma}{\sqrt{n}}\leq \mu\leq \bar{x}+Z\times \frac{\sigma}{\sqrt{n}}[/tex]
For 99% confidence interval Z = 2.576,
Number of weights, n = 50
Substituting
[tex]75-2.576\times \frac{10}{\sqrt{50}}\leq \mu\leq 75+2.576\times \frac{10}{\sqrt{50}}\\\\71.36\leq \mu\leq 78.64[/tex]
The 99% confidence interval for the weights = [71.36lb, 78.64lb]
