- The number of customers entering Jeff's supermarket each morning follows a Poisson distribution.
Past information shows that customers enter at an average rate of 2 every 5 minutes.
Using this information,
- find the probability that exactly 26 customers enter Jeff's supermarket during a randomly selected 1-hour period one morning,
- find the probability that at least 21 customers enter Jeff's supermarket during a randomly selected 1-hour period one morning.
A rival supermarket is opened nearby. Following its opening, the number of customers entering Jeff's supermarket over a randomly selected 40-minute period is found to be 10
- Test, at the 5\% significance level, whether or not there is evidence of a decrease in the rate of customers entering Jeff's supermarket. State your hypotheses clearly.
A further randomly selected 20 -minute period is observed and the hypothesis test is repeated. Given that the true rate of customers entering Jeff's supermarket is now 1 every 5 minutes,
- calculate the probability of a Type II error.