Question

For the following problems, analyze means to specify

1. The sample space S,
2. The probability function P,
3. The events specified (i.e.,list the members of each event), and
4. The probability of each of the events.

Suppose that each time Wayne 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 Wayne charges 4.25,ℎ? ??????? ?? ?? 4.25, he records it as 4, and the round-off error is −0.25,??? ?? ℎ? ?ℎ?????−0.25, but if he charges 4.75, the value recorded is 5 ??? ?ℎ? ?????− ??? ????? ?? 5 and the round−off error is 0.25. Assume this is random, so that each time Wayne charges to his card, he performs a random experiment whose outcome is the round-off error. Assume the outcomes are equiprobable.

Let event A = "at most 3 cents is rounded off in either direction" (i.e., | recorded - actual | ≤ 0.03). Analyze.

Answer 1

Answer:

X follow Uniform 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