Answer to Question #330081 in Statistics and Probability for christian

Question

Supposed 25 respondents were selected from a normal population with a mean of 12.5.

If the sample has a mean of 15.4 and standard deviation of 3, what percentile does the

sample mean represent?

Jon for the

Answer 1

$\mu _{\bar{x}}=\mu =12.5\\\sigma _{\bar{x}}=3\\P\left( \bar{x}\leqslant 15.4 \right) =P\left( \frac{\bar{x}-\mu _{\bar{x}}}{\sigma _{\bar{x}}}\leqslant \frac{15.4-12.5}{3} \right) =\varPhi \left( 0.966667 \right) =0.833\\83.3\% percentile$