Hilda and seven {T} friends attended all four games of T20 cricket games between Pakistan and the West Indies in 201?. As her contribution. she had to purchase eight sandwiches for each of the games on the morning of each match. {a} The rst game was held on Saturday 25th March 2017 in Barbados. She went to the Massy {in Hastings} to get the sandwiches. The manager had informed her that the store has two types of sandwiches, chicken and cheese {sandwiches are not labeled}. He said that past experience had shown that the probability of a customer getting a cheese sandwich is independently 0.3. She selected eight sandwiches at random and paid for them. ii} Determine the probability that the number of cheese sandwiches she bought was: {i} Exactly two {ii} More than 1 {iii} Between 4 and T [6] How many chicken sandwiches does she expect to have bought? [2] The last three games were held in Trinidad. She went to the Massy Store {on French Street} to get the sandwiches. Massy Stores yia a news release has informed the public that the store has two types of sandwiches, chicken and cheese (sandwiches are labeled). They went on to state that past experience had shown that the probability of a customer getting a cheese sandwich is independently [1.4. On Thursday 30th March 201? (late forthe game) Hilda ran into the store and randomly selected eight sandwiches from those on display. pays and leayes the store. Does a binomial distribution proyide an appropriate model for the number of cheese sandwiches Hilda carried to cricket that day? Briey state why. [5] Two of her friends do not eat chicken {the other six people in the group have no preference). When she went to the store on Saturday 1St April 2017, Hilda decided to ensure that there were exactly two cheese sandwiches. If haying selected eight sandwiches at random she finds that they do not include two cheese sandwiches. she replaces the appropriate number of chicken sandwiches with cheese sandwiches. Does a binomial distribution provide an appropriate model for the number of cheese sandwiches Hilda carried to cricket that day? Briey state why. (c) On Sunday 2 April 2017, Hilda again bought eight sandwiches. This time there were four (4) cheese and four (4) chicken sandwiches. The first four friends to eat a sandwich that day, have no preference on the type of sandwich available. Each selected one of the available sandwiches at random and ate it. Does a binomial distribution provide an appropriate model for the number of cheese sandwiches eaten by her friends? Briefly state why. [3]