Mathematics

D 4.x R S 2.x 4 P 2.x B 4 The diagram shows a rectangle, ABCD, where AB = 20 cm and BC = 16 cm. PQRS is a quadrilateral where PB = AS = 2x em, BQ = xem and DR = 4x cm. a Express the area of PQRS in terms of x. b Given that can vary, find the value of x for which the area of PQRS is a minimum and find the magnitude of this minimum area. 5 The diagram shows the graph of 3x + 2y = 30. OPQR is a rectangle with area Acm?. The point is the origin, P lies on the x-axis, R lies on the y-axis and has coordinates (x, y) and lies on the line 3x + 2y = 30. a Show that A = 15x-? b Given that x can vary, find the stationary value of A and determine its nature. R 3x +2y = 30 0 P

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Additional Problem 10. The distribution of exam scores is assumed to be normal with the mean u = 70 and the standard deviation o = 8. (a) What is the probability that the score of a randomly selected student will be between 80 and 84? (b) Six students are randomly selected. What is the probability that exactly two of them score between 80 and 84? (c) Find mo.25 and mo.75, the 0.25th and 0.75th quantiles of the distribution. Compute the interquartile range IQR = m0.75 – Mo.25. Hint: Recall the definition of the pth quantile: P(X 120), (ii) P(X1 > 1.5X2) Answers: (a) 0.0655; (b) 0.0491; (c) mo.25 = 64.6, mo.75 = 75.4, IQR = 10.8.

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APPLYING THE CONCEPTS 2.15 The FIFA World Cup was one of the biggest sporting events of 2018. The file WC2018TeamAge contains the average age of the players (years, in 2018) of the 32 teams that qualified for the event. These average ages were: 26.04 26.78 21.17 27.57 28.17 28.43 28.61 28.96 26.09 27.09 27.26 27.78 28.22 28.43 28.78 29.17 26.09 27.09 27.26 27.83 28.26 28.52 28.83 29.52 26.48 27.09 27.48 28.09 28.35 28.35 28.91 29.74 4. Textbook, Problem 2.15, p.86. Use equal class width of 0.8 and start with 26.0. In addition, draw the corresponding frequency polygon. [Attention: There is a typing mistake in the average ages. It is 27.17 instead of 21.17.]

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Assuming that the relevant distribution is normal, estimate the probability of the following events:

Assuming that the relevant distribution is normal, estimate the probability of the following events: (a) That there will be 70 or more heads in the next hundred flips of a fair coin? (b) That a randomly selected person will weigh over 300 lbs? EXPERT ANSWER A) here this distribution is normal with mean 50 and …

Assuming that the relevant distribution is normal, estimate the probability of the following events: Read More »