The number of cars entering a safari park per 10 -minute period can be modelled by a Poisson distribution with mean 6
Find the probability that in a given 10 -minute period exactly 8 cars will enter the safari park.
Find the smallest value of \(n\) such that the probability that at least \(n\) cars enter the safari park in 10 minutes is less than 0.05
The probability that no cars enter the safari park in \(m\) minutes, where \(m\) is an integer, is less than 0.05
Find the smallest value of \(m\)
A car enters the safari park.
Find the probability that there is less than 5 minutes before the next car enters the safari park.
Given that exactly 15 cars entered the safari park in a 30-minute period,
find the probability that exactly 1 car entered the safari park in the first 5 minutes of the 30-minute period.
Aston claims that the mean number of cars entering the safari park per 10-minute period is more than 6 He selects a 15-minute period at random in order to test whether there is evidence to support his claim.
Determine the critical region for the test at the \(5 \%\) level of significance.