This problem confuses me. Let me explain, because:Originally Posted byjedoob

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From here we see that error is an absolute value thus it is always non-negative.

Thus, when you say that error be no less than .4 do you mean that the error be less than .4

thus, which means henceforth the probability you are trying to find is,

Or do you simply mean to say that error in this case the the difference between the actual and approximate values thus you can have a negative value. Meaning you are trying to find the probability .

In either case let me do both problems.

Let us find the z-score from which is, . Looking up at the tables we have that the probability is, .

Now if you say the first case, then we also need

which is the same because we have symmetry arround the mean. In total we have

Which seems to be the case because that matches your answer.

If it were the other case you need to add because the left hand side of the curve takes exactly half the values. In total you would then have .655