1 The time taken, \(T\) minutes, for a special anti-rust paint to dry was measured for a random sample of 120 painted pieces of metal. The sample mean was 51.2 minutes and an unbiased estimate of the population variance was 37.4 minutes \(^ { 2 }\). Determine a \(99 \%\) confidence interval for the mean drying time.
\(21.5 \%\) of the population of the UK can be classified as 'very tall'.

1. The random variable \(X\) denotes the number of people in a sample of \(n\) people who are classified as very tall. Given that \(\mathrm { E } ( X ) = 2.55\), find \(n\).
2. By using the Poisson distribution as an approximation to a binomial distribution, calculate an approximate value for the probability that a sample of size 210 will contain fewer than 3 people who are classified as very tall.