Answer to Question #169825 in Statistics and Probability for jhon kells

Question

Find n, given that we wish to estimate μ to within 10 units, with 95% confidence, and assuming that σ=100.

Answer 1

$\text{Given that}\\ \sigma=100,E=10,\alpha=0.05,\\ \therefore Z_{\frac{\alpha}{2}}=Z_{0. 025}=1.96\\n=\frac{Z_{\frac{\alpha} {2}}^{2}\times \sigma^{2}} {E^{2}}\\ n=\frac{1.96^{2}\times 100^{2}} {10^{2}} =384.16\approx 385$