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Answer:

[15.375,15.384]

Step-by-step explanation:

#To obtain the error interval, we first need to obtain all numbers than can be rounded off to 15.38.

-Our numbers are (From the lowest):

15.375,15.376,15.377,15.378,15.379,15.380,15.381,15.382,15.383,15.384

From this list, our error interval is [15.375,13.384]

The error interval needed is [15.375, 15.385)

Given that:

A number 'x' rounded to 2 decimal places = 15.38

According to the rules of the rounding of number, we surely know that

x must be in [ 15.375, 15.385) since if x is outside of this interval, then rounding to two places of decimal won't lead to 15.38.

Since x can't be 15.385 itself since that rounds up to 15.39

Or:

[tex]15.375 \leq x < 15.385[/tex]

Thus we have :

[tex]Error \: interval = [15.375,15.385)[/tex]

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