Before 38 16 18 |24 12 30 35 32 31 30 24 35 After 26 15 12 18 24 32 | 14 18 16 18 22 12 a) Calculate the mean and median for each set of data. b) Find the inter-quartile range for each set of data. c) Calculate the standard deviation for each group. d) Compare the distributions. Q-2: [(5+5)+5+5 Marks] a) A jazz band has prepared 18 selections for a concert tour. At each stop, they will perform 10. How many different programs are possible? 11 How many programs are possible if they always begin with the same song and end with the same song? b) How many different ways can 4 tickets be selected from 50 tickets if each ticket wins a different prize? c) In how many ways can 4 people be seated in a circle?Q-3: [4 Marks each] In a recent year there were the following members of licensed drivers in the United States. Male Female Total Age 19 and under 403 451 Age 20 162 155 Age 21 167 162 Total Choose one driver at random. Find the probability that the driver is: a) Female and age 20. b) Age 19 or male c) At most 20 years old? d) Female given that the driver is age 19 and under e) Are the two events female and the driver being age 19 and under independent events? Justify your answer.Q-4: [5+7+5+3Marks] The following table contains the probability distribution for X, the number of traffic accidents reported in a day in Kuwait city. Number of accident: x 1 2 3 14 5 P(X=x)=f(x) 0.1 0.2 0.45 0.15 0.05 0.05 a) What is the expected value of the number of traffic accidents? b) What is the standard deviation of the number of traffic accident? c) Compute the Cumulative Distribution Function. d) What is the probability of having more than 2 traffic accidents in a day? Q-5: [8 +5+3 +4 Marks] The cumulative distribution function of a random variable X is given by F(x) = 1-(Itx)e-* forx20 0 . otherwise a) Find the probability distribution of X. b) Find p(1 5)