Question 2 [20 marks] a) A large proportion of small businesses in the United States have failed during the first few years of operations. On average, 1.6 businesses file for bankruptcy per day in a large city. i. Find the probability that exactly three businesses will file for bankruptcy on a given day in this city. [3 marks] ii. What is the probability that at least one business will file for bankruptcy on a given day in this city? [3 marks] b) The owner of the new ice cream chain Cool Ice would like to understand the effect atmosphere temperature has on ice cream sales during summer. A sample of ice cream sales on 21 consecutive days was selected and the scatterplot of temperature (in Celsius) versus ice cream sales (in $100), together with the equation of a fitted regression line, is shown below. Ice Cream Sales vs Temperature Ice Cream Sales ('00s) 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 15 20 25 30 y= 0.1093x 0.5917 R2=0.94 Temperature (Degrees Celsius) 35 40 i. What is the value of the slope and what does it measure? [3 marks] ii. What is the value of the intercept and what does it measure? What do you think about this value? [4 marks] iii. What is the value of the coefficient of determination and what does it mean? [3 marks] iv. Calculate the correlation coefficient and interpret your result. [4 marks]