3 In the manufacture of child car seats, a resin made up of three ingredients is used. The ingredients are two polymers and an impact modifier. The resin is prepared in batches. Each ingredient is supplied by a separate feeder and the amount supplied to each batch, in kg, is assumed to be Normally distributed with mean and standard deviation as shown in the table below. The three feeders are also assumed to operate independently of each other.

1. Find the probability that, in a randomly chosen batch of resin, there is no more than 2100 kg of polymer 1.
2. Find the probability that, in a randomly chosen batch of resin, the amount of polymer 1 exceeds the amount of polymer 2 by at least 400 kg .
3. Find the value of \(b\) such that the total amount of the ingredients in a randomly chosen batch exceeds \(b \mathrm {~kg} 95 \%\) of the time.
4. Polymer 1 costs \(\pounds 1.20\) per kg, polymer 2 costs \(\pounds 1.30\) per kg and the impact modifier costs \(\pounds 0.80\) per kg. Find the mean and variance of the total cost of a batch of resin.
5. Each batch of resin is used to make a large number of car seats from which a random sample of 50 seats is selected in order that the tensile strength (in suitable units) of the resin can be measured. From one such sample, the \(99 \%\) confidence interval for the true mean tensile strength of the resin in that batch was calculated as \(( 123.72,127.38 )\). Find the mean and standard deviation of the sample.