5. A delivery company loses packages randomly at a mean rate of 10 per month.
The probability that the delivery company loses more than 12 packages in a randomly selected month is \(p\)
- Find the value of \(p\)
The probability that the delivery company loses more than \(k\) packages in a randomly selected month is at least \(2 p\)
- Find the largest possible value of \(k\)
In a randomly selected month,
- find the probability that exactly 4 packages were lost in each half of the month.
In a randomly selected two-month period, 21 packages were lost.
- Find the probability that at least 10 packages were lost in each of these two months.
- Using a suitable approximation, find the probability that more than 27 packages are lost during a randomly selected 4-month period.