3 A machine fills bags with frozen peas. Measurements taken over several weeks have shown that the standard deviation of the weights of the filled bags of peas has been 2.2 grams. Following maintenance on the machine, a quality control inspector selected 8 bags of peas. The weights, in grams, of the bags were $$\begin{array} { l l l l l l l l } 910.4 & 908.7 & 907.2 & 913.2 & 905.6 & 911.1 & 909.5 & 907.9 \end{array}$$ It may be assumed that the bags constitute a random sample from a normal distribution.

1. Giving the limits to four significant figures, calculate a 95\% confidence interval for the mean weight of a bag of frozen peas filled by the machine following the maintenance:
   1. assuming that the standard deviation of the weights of the bags of peas is known to be 2.2 grams;
   2. assuming that the standard deviation of the weights of the bags of peas may no longer be 2.2 grams.
2. The weight printed on the bags of peas is 907 grams. One of the inspector's concerns is that bags should not be underweight. Make two comments about this concern with regard to the data and your calculated confidence intervals.
   [0pt] [2 marks]