3. A market trader sells ball-point pens on his stall. He sells the pens for a different fixed price, x pence, in each of six weeks. He notes the number of pens, y, that he sells in each of these six weeks. The results are shown in the table below: X y 10 68 15 60 20 55 25 48 30 38 35 323} Calculate and interpret the values for beta (slope coefficient) and alpha (intercept) for the Least Squares Regression Line. [8 marks] b) Write out the regression equation. [1 mark] c) If the market trader sells the pens for 28 dollars in week 7, how many pens will the market trader sell for that week? [1 mark] Question 4 Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. Have Shopped Have Never Shopped Total Male 500 700 1200 Female 300 500 800 Total 800 1200 2000 a) If one adult is selected at random from these 2000 adults, find the probability that this adult: i. has never shopped on the Internet. [1 mark] ii. is a male. [1 mark] lii. has shopped on the Internet given that this adult is a female. [1 mark] iv. is a male given that this adult has never shopped on the internet. [1 mark]1)} Are the events \"Have shopped\" and \"Male\" mutually exclusive? Why or why not? [2 marks] 6) Are the events \"Male\" and \"Male\" mutually exclusive? Why or why not? [2 marks] d) Are the events \"Female\" and \"Have Shopped\" independent? Why or why not? [2 marks]