Please solve this.

Consider the following sample of entry level salaries of recent computing major graduates from University of Buckingham. Graduate 2 6 8 9 Salary (thousand GBP) 1 . ON OWN 3 0o (a) -20 marks Compute the mean, median, mode, variance, standard deviation, range and inter-quartile range for the given data. (b) - 10 marks Use a box plot to illustrate the above data. Question 2 (35 marks) (a) - 10 marks A black and a blue die are rolled (both fair and six sided). What is the probability that the sum of their numbers is 5 and that the number on the blue die is larger than the number on the black die? Let A be the event that the number on the blue die is larger than the number on the black die, and let B be the event that the sum is 5. Are A and B independent events? (b) - 10 marks From a normal deck of cards (52 cards altogether), two cards are drawn at random (without replacement). What is the probability of drawing at least one ace? c) - 15 marks A bag consists of 2 blue, 5 green and 5 red balls. At random 3 balls are picked out of the bag one by one and without replacement. Compute the probability of picking at least 2 green balls. Question 3 (35 marks) A farmer from Buckingham has gone duck hunting. When she fires her gun at a duck, the probability of a hit is . On a typical duck hunt the farmer will fire her gun 45 times. Let X denote the number of shots hitting a duck on a typical hunt. (a) - 5 marksAssuming the shots are fired independently, explain what distribution X will follow (b) - 10 marksWhat is the probability that at least 10 of the farmer's shots are hits? (c)- 10 marks What is the probability that the farmer scores between 5 and 15 hits, both included? (d) - 10 marksWhat is the probability that the farmer achieves at least one hit