a)
From a standard normal distribution table we have that:
[tex]P(z>1.3)=0.0968[/tex]
b)
In this case we need to use the z-score defined as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where mu is the mean, sigma is the standard deviation and x is the value we are looking for; in this case we would have:
[tex]\begin{gathered} P(X<85)=P(z<\frac{85-89}{11}) \\ =P(z<-0.3636) \\ =0.3581 \end{gathered}[/tex]
Therefore:
[tex]P(X<85)=0.3581[/tex]
c)
Using the method in the previous part and the probability properties we have:
[tex]\begin{gathered} P(71d)
To find how many teams we find the probability and multiply by the population:
[tex]\begin{gathered} 30P(X>76)=30P(z>\frac{76-89}{11}) \\ =30P(z>-1.1818) \\ =30(0.8183) \\ =24.54 \end{gathered}[/tex]
Therefore approximately 25 teams have at least 76 points.
