1 A garage sells tyres. The number of customers arriving at the garage to buy tyres in a 10-minute period is modelled by a Poisson distribution with mean 2
- Find the probability that
- fewer than 4 customers arrive to buy tyres in the next 10 minutes,
- more than 5 customers arrive to buy tyres in the next 10 minutes.
The manager randomly selects 20 non-overlapping, 30-minute periods.
- Find the probability that there are between 4 and 7 (inclusive) customers arriving to buy tyres in exactly 15 of these 30-minute periods.
The manager believes that placing an advert in the local paper will lead to a significant increase in the number of customers arriving at the garage.
A week after the advert is placed, the manager randomly selects a 25 -minute period and finds that 10 customers arrive at the garage to buy tyres. - Test, at the \(5 \%\) level of significance, whether or not there is evidence to support the manager's belief.
State your hypotheses clearly. - Explain why the Poisson distribution is unlikely to be valid for the number of tyres sold during a 10-minute period.