10 packages have the following weights 464 461 458 470 461 4

10 packages have the following weights: 46.4, 46.1, 45.8, 47.0, 46.1, 45.9, 45.8, 45.9, 46, 45.2

Solution

Getting the sample standard deviation,

s = sample standard deviation =    0.461398839

As              
              
df = n - 1 =    9          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    19.0227678          
chi^2(alpha/2) =    2.7003895          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.10072141          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.709527273          
              
Thus, the confidence interval for the variance is              
              
(   0.10072141   ,   0.709527273   ) [ANSWER]