Question 1204602
x̄ = {{{12.3 }}} => mean length

sample size {{{n=  46}}}
 
population mean {{{mu= 13.5 }}}

standard deviation {{{sigma= 3.4}}}


 to find: {{{P}}}(x̄ > {{{12.3}}})


z-statistic:  (x̄ -{{{mu}}})/{{{(sigma/sqrt(n))}}}


compute z-statistic for x̄ = {{{12.3 }}}


{{{z = (12.3 - 13.5)/(3.4/sqrt(46)) = -2.393763523456}}}


 {{{P(z > -2.393763523456) =  0.99166175}}}  =>{{{99.166175}}}% chance of the sample mean being greater than {{{12.3 }}}inches long