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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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 radiusr inscribed. The computer generates points, at random, within the
square.
(a) Show that the probability that a point lies within the circle is exactly-
4
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 -
(c) Obtain an approximate 90% confidence interval for
and hence an
approximate 90% confidence interval for 7.
(d) Estimate the minimum number of points that the computer must generate in
with a sampling error of
4
order to construct a 90% confidence interval for
0.01.
Transcribed Image Text: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 radiusr inscribed. The computer generates points, at random, within the square. (a) Show that the probability that a point lies within the circle is exactly- 4 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 - (c) Obtain an approximate 90% confidence interval for and hence an approximate 90% confidence interval for 7. (d) Estimate the minimum number of points that the computer must generate in with a sampling error of 4 order to construct a 90% confidence interval for 0.01.
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