Answer to Question #200780 in Statistics and Probability for Nivrutti K Shelawa

Question

If population mean and standard deviation is 100 and 10 respectively. And sample mean is 115 and n = 30 then what is z score?

Answer 1

Z score formula for the mean of n observation

$\\z=\frac{\bar x-\mu}{(\frac{\sigma}{\sqrt{n}})}$

$\mu =100\\ \sigma=10\\ \bar x=115\space \\ n=30$

$\\z=\frac{115-100}{(\frac{10}{\sqrt{30}})}\\ \\z=\frac{15}{1.82574186}\\ z=8.21584061$