2024 EJC H1 Q12

In a supermarket, ducks and turkeys are sold by mass. The masses, in kilograms, of ducks and turkeys have independent normal distributions with means and standard deviations as shown in the table.

1. Find the probability that the mass of a randomly chosen duck is less than \(5\)% below the mean mass.[2]
2. Find the probability that mean mass of \(3\) randomly chosen ducks and \(2\) randomly chosen turkeys is between \(4.7\) kilograms and \(5.48\) kilograms.[3]

Ducks are sold at \(\$8.35\) per kilogram and turkeys are sold at \(\$18.25\) per kilogram.

3. Cayson thinks that there is at most \(70\)% chance that a randomly chosen turkey costs at least \(\$70.25\) more than a randomly chosen duck. Determine whether Cayson is correct, justifying your answer with workings.[3]

A 'poultry pack' consists of a randomly chosen duck and a randomly chosen turkey. A 'poultry pack' is considered expensive if it costs more than \(\$150\).

4. Find the probability that in \(13\) randomly selected 'poultry packs', less than half of them are expensive.[4]