And 2 cm for 5 grams on the horizontal axis 80 70 60

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Unformatted text preview: ............ (Total 3 marks) 214 307. A machine produces packets of sugar. The weights in grams of thirty packets chosen at random are shown below. Weight (g) Frequency 29.6 29.7 29.8 29.9 30.0 30.1 30.2 30.3 2 3 4 5 7 5 3 1 Find unbiased estimates of (a) the mean of the population from which this sample is taken; (b) the variance of the population from which this sample is taken. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 215 308. The nth term, un, of a geometric sequence is given by un = 3(4)n+1, n ∈ + . (a) Find the common ratio r. (b) Hence, or otherwise, find Sn, the sum of the first n terms of this sequence. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 309. Let f : x a sin x , π ≤ x ≤ 3π . Find the area enclosed by the graph of f and the x-axis. x Working: Answers: ………………………………………….. (Total 3 marks) 216 310. Find the equation of the line of intersection of the two planes –4x + y + z = –2 and 3x – y + 2z = –1. Working: Answers: ………………………………………….. (Total 3 marks) 311. (z + 2i) is a factor of 2z3–3z2 + 8z – 12. Find the other two factors. Working: Answers: ………………………………………….......... ........................................................................... (Total 3 marks) 217 312. Given that P ( X ) = (a) P(Y′); (b) 2 1 , P(Y X ) = P(Y X ′) = , , find 3 4 P(X′ ∪ Y′). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 313. Find an equation of the plane containing the two lines x –1= 1– y x +1 2 – y z+2 = z – 2 and = = . 2 3 3 5 Working: Answers: ………………………………………….. (Total 3 marks) 218 314. Z is the standardised normal random variable with mean 0 and variance 1. Find the value of a such that P( | Z | ≤ a) = 0.75. Working: Answers: ………………………………………….. (Total 3 marks) 315. Given that z = (b + i)2, where b is real and positive, find the exact value of b when arg z = 60°. Working: Answers: ………………………………………….. (Total 3 marks) 219 316. X is a binomial random variable, where the number of trials is 5 and the probability of success of each trial is p. Find the values of p if P(X = 4) = 0.12. Working: Answers: ………………………………………….. (Total 3 marks) 317. Find the general solution of the differential equation dx = kx(5 – x) where 0 < x < 5 , and k is dr a constant. Working: Answers: ………………………………………….. (Total 3 marks) 220 318. An astronaut on the moon throws a ball vertically upwards. The height, s metres, of the ball, after t second...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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