(10points) In the following table x is a random variable representing the miles driven on a street with a 25 mph while y presents the miles per gallon. 45 25 15 30 Y 20 50 40 45 25 a) (4 Points) Draw a scatter diagram labe axes appropriately and choose a consistent scale. b) (2 Points) Based on the scatter diagram, would you estimate the correlation coefficient to be positive close to zero or negative? c) (4 Points) Give an approximate value of the correlation coemcient. 7) (12 points) it is estimated that 80% of a grapenuit crop is good, the other 20% have rotten centers that cannot be detected until the grapefruit are cut open. The grapefruits are sold in sacks of 10 a) (3 Points) What is the probability of getting exactly 9 good grapefruit in a sack? b) (3 Points) What is the probability of getting at least 9 good grapefruit in a sack? c) (3 Points) Find the expected value: d) (3 Points) Find the standard deviation: