We are going to use the normal standard distribution to resolve this exercise, in that sense, finding the z value is necessary. Doing the calculations, we get
[tex]\begin{gathered} z=\frac{\frac{x-\bar{x}}{s}}{\sqrt{n}} \\ z=\frac{\frac{2.15-2.3}{1.1}}{\sqrt{40}} \\ z=\frac{\frac{-3}{22}}{2\sqrt{10}}\approx-0.0215609 \end{gathered}[/tex]Now it only remains to calculate the probability, using a normal distribution calculator or a normal distribution table as follows
[tex]P(z<-0.0216)\approx0.4914[/tex]Thus, the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.15 penalties per game or less is 0.4914
