Final answer:
The minimum number of terms needed to approximate the sum with |error| < 0.001 can be found using the error bound formula.
Step-by-step explanation:
The minimum number of terms needed to approximate the sum with |error| < 0.001 can be found using the error bound formula. The error bound formula states that the maximum error is equal to the standard deviation multiplied by the critical value. In this case, we want the maximum error to be less than 0.001. So we can rearrange the formula to solve for the sample size n as:
n ≥ (critical value * standard deviation) / maximum error
By plugging in the values for the standard deviation and maximum error, and looking up the critical value for the desired confidence level, you can determine the minimum number of terms needed to approximate the sum with the specified error tolerance.