2022 NYJC P2 Q8
A shooter can hit the bullseye of his target $7$ out of $10$ attempts on average. In a particular training, he made $35$ attempts on the target.
(i)
State two assumptions for the number of bullseyes achieved in a training to be well modelled by a binomial distribution.
[2]
(ii)
Explain why one of these assumptions stated in part (i) may not hold in this context.
[1]
Assume now that the number of bullseyes the shooter achieved in a training follows a binomial distribution.
(iii)
Given that $m$ is the most probable number of bullseyes the shooter can achieve in a training, find the value of $m$ and state its corresponding probability.
[2]
(iv)
Find the probability that the shooter achieves at least $25$ bullseyes in a training.
[2]
(v)
The shooter attended $40$ trainings. Using a suitable approximation, find the probability that he achieved an average of at least $25$ bullseyes per training.
[3]
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