In a shop customers who pay with cash have the final price rounded to the closest five cents(in other words purchase is payed in five cent accuracy). Lets assume that the "loss" caused by a customer paying in cash after rounding the final price in cents (=X) is continuously uniformly distributed u[-2.5,2.5]. In the shop 1000 of the visiting customers pay in cash.

What is the probability that the loss caused by the rounding of the final price (in other words X1 + X2 +...+X1000) is at least $1?

Question

In a shop customers who pay with cash have the final price rounded to the closest five cents(in other words purchase is payed in five cent accuracy). Lets assume that the "loss" caused by a customer paying in cash after rounding the final price in cents (=X) is continuously uniformly distributed u[-2.5,2.5]. In the shop 1000 of the visiting customers pay in cash.

What is the probability that the loss caused by the rounding of the final price (in other words X1 + X2 +...+X1000) is at least $1?