In a manufacturing plant, a production line operates to fill the bag with 5 kg of rice. A quality control inspector checks a random sample of 28 bags. The weight of rice (kg) in each bag is recorded...

In a manufacturing plant, a production line operates to fill the bag with 5 kg of rice. A quality control inspector checks a random sample of 28 bags. The weight of rice (kg) in each bag is recorded as follow: 5.02 5.01 4.98 4.97 5.02 5.03 4.96 5.01 5.00 5.04 4.97 4.92 5.03 5.05 5.02 5.01 5.00 4.96 4.97 4.99 4.96 5.01 5.02 4.98 5.00 5.02 5.00 4.98 Assume the weight of rice in a bag is normally distributed. (a) Construct a 98% confidence interval estimate of the population mean weight of rice in a bag.  (b) For random samples, each with sample size 28, will be selected periodically. Suppose the 98% confidence interval estimate of the population mean weight of rice in a bag have been constructed for 800 independent samples. Approximately how many such intervals can successfully include the true unknown population mean?