Final answer:
To estimate a population mean within ± 60 of the true mean value using a confidence level of 95%, a sample size of at least 182 is needed.
Step-by-step explanation:
To estimate a population mean within ± 60 of the true mean value using a confidence level of 95%, we need to determine the required sample size. The formula to calculate the sample size is:
n = (Z² * σ²) / E²
Where:
n is the required sample size,
Z is the Z-score corresponding to the chosen confidence level (in this case, it is 1.96 for 95% confidence),
σ is the known population variance (140,625 in this case), and
E is the desired margin of error (60 in this case).
Substituting the values into the formula, we get:
n = (1.96² * 140,625) / 60² = 181.44.
Therefore, we would need a sample size of at least 182 to estimate the population mean within ± 60 with 95% confidence.