Question

in a study conducted by national telecommunication commission (NTC), the average internet speed of Philippines is 10.5 mbps and standard deviation of 1.1mbps. what is the probability that a random sample of 100 user will have combined Internet speed between 8.4 mbps and 9.4 mbps

Answer 1

$P\left( 8.4<\bar{x}<9.4 \right) =P\left( \sqrt{n}\frac{8.4-\mu}{s}<\sqrt{n}\frac{\bar{x}-\mu}{s}<\sqrt{n}\frac{9.4-\mu}{s} \right) =\\=P\left( \sqrt{100}\frac{8.4-10.5}{1.1}<Z<\sqrt{100}\frac{9.4-10.5}{1.1} \right) =\\=\varPhi \left( -10 \right) -\varPhi \left( -19.0909 \right) =7.6\cdot 10^{-24}-1.3\cdot 10^{-81}=7.6\times 10^{-24}$