Question 5 [20 marks] a) A direct marketing company believes that the probability of making a...

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Question 5 [20 marks] a) A direct marketing company believes that the probability of making a sale when a call is made to an individual's home is 0.15. i. What is the probability of making 2 or 3 sales in a sample of 20 calls? [3 marks] ii. What is the probability of making at least one sale in a sample of 20 calls? [2 marks] iii. Find the expected number of sales in a sample of 30 calls. Explain. [3 marks] b) The table below indicates the opinion of a sample of 200 people classified by gender on the recent decision to increase in the fuel price. Opinion on the fuel price Gender Agree Neutral Disagree Female 38 54 12 Male 12 36 48 If a person is selected at random from this group, compute the probability that this person i. is neutral to the decision. [2 marks] ii. is a male or against the decision. iii. is a female given that she agrees to the decision. [2 marks] [3 marks] iv. Are Gender and Opinion on the fuel price statistically independent? [5 marks] Question 5 [20 marks] a) A direct marketing company believes that the probability of making a sale when a call is made to an individual's home is 0.15. i. What is the probability of making 2 or 3 sales in a sample of 20 calls? [3 marks] ii. What is the probability of making at least one sale in a sample of 20 calls? [2 marks] iii. Find the expected number of sales in a sample of 30 calls. Explain. [3 marks] b) The table below indicates the opinion of a sample of 200 people classified by gender on the recent decision to increase in the fuel price. Opinion on the fuel price Gender Agree Neutral Disagree Female 38 54 12 Male 12 36 48 If a person is selected at random from this group, compute the probability that this person i. is neutral to the decision. [2 marks] ii. is a male or against the decision. iii. is a female given that she agrees to the decision. [2 marks] [3 marks] iv. Are Gender and Opinion on the fuel price statistically independent? [5 marks]