There is a special calculator that when used to add numbers up, it always rounds up...

There is a special calculator that when used to add numbers up, it always rounds up or down the number to the closest integer and ignore the decimals. For example, you want to add 1.1+2+3.6, it will show can calculate as 1+2+4, etc. Assume the error from each adding follows uniform distribution on (-0.5, 0.5).

When adding 1500 numbers together, what is the probability of the absolute value of total error is greater than 15?
How many numbers can you add until the probability of the absolute value of total error being less than 10 reaches 0.9?

(hint, you may need to find the expectation and the variance of uniform distribution, and using CLT for your calculation)

Expert Solution

orchestra answered 1 year ago

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