5 When Nina does the weekly grocery shopping she models the total cost by adding up the cost of each item in her head as she goes along. To simplify matters she rounds the cost of each item to the nearest pound. One week Nina buys 48 items.

1. Calculate the maximum possible error in Nina's model in this case. Nina estimated the total cost of her shopping to be \(\pounds 92\). The actual cost is \(\pounds 90.23\).
2. Explain whether this is consistent with Nina’s model. The next week her husband, Kareem, does the weekly shopping. He models the total cost by chopping the cost of each item to the nearest pound as he goes along. On this occasion Kareem buys 52 items.
3. Calculate the expected error in Kareem's model in this case. Using his model Kareem estimates the total cost as \(\pounds 76\). The total cost of the shopping is \(\pounds 103.24\).
4. Explain how such a large error could arise. The next week Kareem buys \(n\) items.
5. Write down a formula for the maximum possible error when Kareem uses his model to estimate the total cost of his shopping.
6. Explain how Kareem's model could be adapted so that his formula gives the same expected error as Nina's model when they are both used to estimate the total cost of the shopping.