Question 3: Suppose that each time Lamar charges an item to his credit card, he

Question

Question 3: Suppose that each time Lamar charges an item to his credit card, he rounds the amount to the nearest dollar in his records (assume that for x dollars, the amount x.50 is rounded to x + 1 dollars). The round-off error is defined as (recorded - actual); the units are dollars, so if Lamar charges $4.25, he records it as $4, and the round-off error is $-0.25, but if he charges $4.75, the value recorded is $5 and the round-off error is $0.25. Assume this is random, so that each time Lamar charges to his card, he performs a equiprobable random experiment whose outcome is the round-off error. Let event A = "at most 3 cents is rounded off in either direction" (i.e., | recorded - actual | 0.03). Analyze.

Explanation / Answer

X follow Unifiform distribution (-1/2,1/2)

f(x) = 1   -1/2 < x< 1/2

P(|x| < 0.03)

= P(-0.03 < X< 0.03)

= (0.03 -(-0.03)) = 0.06

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