4 At a parcel delivery company it is known that the probability that a parcel is delivered to the wrong address is 0.0005 . On a particular day, 15000 parcels are delivered. The number of parcels delivered to the wrong address is denoted by the random variable \(X\).

1. Explain why the binomial distribution and the Poisson distribution could both be suitable models for the distribution of \(X\).
2. Use a Poisson distribution to find each of the following.
   • \(\mathrm { P } ( X = 5 )\)
   • \(\mathrm { P } ( X \geqslant 8 )\)
   You are given that 15000 parcels are delivered each day in a 5-day working week.
3. 1. Determine the probability that at least 40 parcels are delivered to the wrong address during the week.
   2. Determine the probability that at least 8 parcels are delivered to the wrong address on each of the 5 days in the week.