1993 Paper 2 Q15

Year: 1993
Paper: 2
Question Number: 15

Course: LFM Stats And Pure
Section: Continuous Uniform Random Variables

Difficulty: 1600.0 Banger: 1501.4

probability continuous uniform distribution central limit theorem normal approximation rounding error summation variance calculation

Problem

Two computers, LEP and VOZ are programmed to add numbers after first approximating each number by an integer. LEP approximates the numbers by rounding: that is, it replaces each number by the nearest integer. VOZ approximates by truncation: that is, it replaces each number by the largest integer less than or equal to the number. The fractional parts of the numbers to be added are uniformly and independently distributed. (The fractional part of a number \(a\) is \(a-\left\lfloor a\right\rfloor ,\) where \(\left\lfloor a\right\rfloor \) is the largest integer less than or equal to \(a\).) Both computers approximate and add 1500 numbers. For each computer, find the probability that the magnitude of error in the answer will exceed 15. How many additions can LEP perform before the probability that the magnitude of error is less than 10 drops below 0.9?

No solution available for this problem.

Rating Information

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1501.4

Banger Comparisons: 2

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Problem source

Two computers, LEP and VOZ are programmed to add numbers after first
approximating each number by an integer. LEP approximates the numbers
by rounding: that is, it replaces each number by the nearest integer.
VOZ approximates by truncation: that is, it replaces each number by
the largest integer less than or equal to the number. The fractional
parts of the numbers to be added are uniformly and independently distributed.
(The fractional part of a number $a$ is $a-\left\lfloor a\right\rfloor ,$
where $\left\lfloor a\right\rfloor $ is the largest integer less
than or equal to $a$.) Both computers approximate and add 1500 numbers.
For each computer, find the probability that the magnitude of error
in the answer will exceed 15. 

How many additions can LEP perform before the probability that the
magnitude of error is less than 10 drops below 0.9?

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