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.
5 (a) 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 $X$.\\
(i) State, with a justification, a suitable approximating distribution for $X$, giving the values of any parameters.\\
(ii) Use the approximating distribution to calculate $\mathrm { P } ( X > 0 )$.\\
(b) 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.\\
\hfill \mbox{\textit{CAIE S2 2021 Q5}}