Question

the allowance of junior high school students is normally distributed has a mean of 18.3 pesos and standard deviation of 1.5 pesos. if 60 samples consisting og 13 JHS each are drawn from the population,what is the mean and standard deviation of the sampling distribution of means? assume that the population is infinite.

Answer 1

$n=13 - the\ size\ of\ each\ sample\\X\sim N\left( 18.3,\frac{1.5}{\sqrt{13}} \right) -distribution\,\,of\,\,each\,\,means\\N=60\\\mu _{\bar{X}}=\mu =18.3\\\sigma _{\bar{X}}=\frac{\sigma _X}{\sqrt{N}}=\frac{1.5}{\sqrt{13\cdot 60}}=0.0537086\\$