7. A research student studying numerical analysis desires to use a computer to estimate the value of a . The diagram shows a square computer screen with a circle of radius r inscribed. The computer generates points, at random, within the square. π (a) Show that the probability that a point lies within the circle is exactly- The computer generates 1000 points randomly. It is found that 786 of the points fall within the circle. (b) Find the point estimate of the proportion- 4 (c) Obtain an approximate % confidence interval for and hence an approximate 90% confidence interval for .

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