The proportion of people having a particular medical condition is 1 in 100000 . A random sample of 2500 people is obtained. The number of people in the sample having the condition is denoted by \(X\).
State, with a justification, a suitable approximating distribution for \(X\), giving the values of any parameters.
Use the approximating distribution to calculate \(\mathrm { P } ( X > 0 )\).
The percentage of people having a different medical condition is thought to be \(30 \%\). A researcher suspects that the true percentage is less than \(30 \%\). In a medical trial a random sample of 28 people was selected and 4 people were found to have this condition.
Use a binomial distribution to test the researcher's suspicion at the \(2 \%\) significance level.