Q5 \ I need only help with d) e) f)
Q6 \ I need help with e) f) g)
Leave blank 6. The random variable A represents the score when a spinner is spun. The probability distribution for A is given in the following table. a 5 7 P(A = a) 0.40 0.20 0.25 0.15 (a) Show that E(A) = 3.5 DO NOT WRITE IN THIS AREA (2) (b) Find Var(A) (3) The random variable B represents the score on a 4-sided die. The probability distribution for B is given in the following table where & is a positive integer. b 3 4 k P(B = b) 0.25 0.25 0.25 0.25 (c) Write down the name of the probability distribution of B. (1) (d) Given that E(B) = E(A) state, giving a reason, the value of k. (1) DO NOT WRITE IN THIS AREA The random variable X ~ N(u, o?) Sam and Tim are playing a game with the spinner and the die. They each spin the spinner once to obtain their value of A and each roll the die once to obtain their value of B. Their value of A is taken as their value of u and their value of B is taken as their value of o. The person with the larger value of P(X > 3.5) is the winner. (e) Given that Sam obtained values of a = 4 and b = 3 and Tim obtained b = 4 find, giving a reason, the probability that Tim wins. (2) (f) Find the largest value of P(X > 3.5) achievable in this game. ( 4) DO NOT WRITE IN THIS AR (g) Find the probability of achieving this value. (2)Leave blank 5. A large company rents shops in different parts of the country. A random sample of 10 shops was taken and the floor area, x in 10m', and the annual rent, y in thousands of dollars, were recorded. The data are summarised by the following statistics [x = 900 Ex = 84818 Ey= 183 Ey = 3434 and the regression line of y on x has equation y = 6.066 + 0.136x DO NOT WRITE IN THIS AREA (a) Use the regression line to estimate the annual rent in dollars for a shop with a floor area of 800 m3 (2) (b) Find S, and S. (3) (c) Find the product moment correlation coefficient between y and x. (4) An 11th shop is added to the sample. The floor area is 900m and the annual rent is 15 000 dollars. (d) Use the formula S= _(x -x)(y - y) to show that the value of S, for the 11 shops will be the same as it was for the original 10 shops. (2) DO NOT WRITE IN THIS AREA (e) Find the new equation of the regression line of y on x for the 11 shops. (3) The company is considering renting a larger shop with area of 3000 m- (f) Comment on the suitability of using the new regression line to estimate the annual rent. Give a reason for your answer. (1)
