For this problem, we are told that a certain set of scores is normally distributed with a mean of 71.9 and standard deviation of 10.1 points. We need to determine the score that will determine the boundary for F grades, if they are the lowest 11%.
The first step we need to take is determine the z-score that represent the lowest 11% on the distribuition. We have:
[tex]Z(z<-1.23)=0.1093[/tex]The closest value to 11% on the z-table is a z-score of -1.23, which produces a percentage of 10.93%. With this we can use the expression for the z-score in order to determine the grade that represents this:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ -1.23=\frac{x-71.9}{10.1}\\ \\ x-71.9=-12.423\\ \\ x=71.9-12.423=59.48 \end{gathered}[/tex]The score that will determine the boundary of the F grade is 59.48.
