A company rounds its losses to the nearest dollar. The error on each loss is independently and uniformly distributed on [–0.5, 0
.5]. If the company rounds 2000 such claims, find the 95th percentile for the sum of the rounding errors.
1 answer:
Answer:
the 95th percentile for the sum of the rounding errors is 21.236
Step-by-step explanation:
Let consider X to be the rounding errors
Then;
where;
a = -0.5 and b = 0.5
Also;
Since The error on each loss is independently and uniformly distributed
Then;
where;
n = 2000
Mean
Recall:
For 95th percentile or below
From Normal table; Z > 1.645 = 0.05
the 95th percentile for the sum of the rounding errors is 21.236
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