Standard +0.3 This is a straightforward application of standard Poisson distribution techniques (scaling rates, adding independent Poisson processes, memoryless property, and normal approximation to binomial). All parts follow textbook procedures with no novel problem-solving required, making it slightly easier than average for Further Maths statistics.
Dave and Llinos like to go fishing. When they go fishing, on average, Dave catches 4.3 fish per day and Llinos catches 3.8 fish per day. A day of fishing is assumed to be 8 hours.
(i) Calculate the probability that they will catch fewer than 2 fish in total on a randomly selected half-day of fishing.
(ii) Justify any distribution you have used in answering (a)(i).
On a randomly selected day, Dave starts fishing at 7 am. Given that Dave has not caught a fish by 11 am,
find the expected time he catches his first fish,
calculate the probability that he will not catch a fish by 3 pm .
On average, only \(2 \%\) of the fish that Llinos catches are trout. Over the course of a year, she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3] [0pt]
she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3]
State, with a reason, a distribution, including any parameters, that could approximate the distribution used in part (c).
\begin{enumerate}
\item Dave and Llinos like to go fishing. When they go fishing, on average, Dave catches 4.3 fish per day and Llinos catches 3.8 fish per day. A day of fishing is assumed to be 8 hours.\\
(a) (i) Calculate the probability that they will catch fewer than 2 fish in total on a randomly selected half-day of fishing.\\
(ii) Justify any distribution you have used in answering (a)(i).\\
(b) On a randomly selected day, Dave starts fishing at 7 am. Given that Dave has not caught a fish by 11 am,\\
(i) find the expected time he catches his first fish,\\
(ii) calculate the probability that he will not catch a fish by 3 pm .\\
(c) On average, only $2 \%$ of the fish that Llinos catches are trout. Over the course of a year, she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3]\\[0pt]
she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3]\\
(d) State, with a reason, a distribution, including any parameters, that could approximate the distribution used in part (c).\\
\end{enumerate}
PLEASE DO NOT WRITE ON THIS PAGE\\
\hfill \mbox{\textit{WJEC Further Unit 2 2024 Q1 [14]}}