Xena catches fish at random, at a constant rate of 0.6 per hour.
Find the probability that Xena catches exactly 4 fish in a 5 -hour period.
The probability of Xena catching no fish in a period of \(t\) hours is less than 0.16
Find the minimum value of \(t\), giving your answer to one decimal place.
Independently of Xena, Zion catches fish at random with a mean rate of 0.8 per hour.
Xena and Zion try using new bait to catch fish. The number of fish caught in total by Xena and Zion after using the new bait, in a randomly selected 4-hour period, is 12
Use a suitable test to determine, at the \(5 \%\) level of significance, whether or not there is evidence that the rate at which fish are caught has increased after using the new bait. State your hypotheses clearly and the \(p\)-value used in your test.