4 Rice that can be cooked in microwave ovens is sold in packets which the manufacturer claims contain a mean weight of more than 250 grams of rice. The weight of rice in a packet may be modelled by a normal distribution. A consumer organisation's researcher weighed the contents, \(x\) grams, of each of a random sample of 50 packets. Her summarised results are: $$\bar { x } = 251.1 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 184.5$$

1. Show that, correct to two decimal places, \(s = 1.94\), where \(s ^ { 2 }\) denotes the unbiased estimate of the population variance.
2. 1. Construct a \(96 \%\) confidence interval for the mean weight of rice in a packet, giving the limits to one decimal place.
   2. Hence comment on the manufacturer's claim.
3. The statement '250 grams' is printed on each packet. Explain, with reference to the values of \(\bar { x }\) and \(s\), why the consumer organisation may consider this statement to be dubious.