Answer:
(a) 84.2
(b) 10.6
Step-by-step explanation:
To solve this questions we can use the standardization formula, where we know that if [tex]X\sim N(\mu,\sigma^2)[/tex] then [tex]Z=\frac{X-\mu}{\sigma} \sim N(0,1)[/tex]
So for
(a) we know that the z score for the 70th percentile is 0.524, so using the normalization equation we have
[tex]\frac{X-\mu}{\sigma}=0.524[/tex]
[tex]X=0.524*8+80=84.192[/tex]
(b) We can procede as above and get
[tex]P(X<70)=P(\frac{X-80}{8}<\frac{70-80}{8})=P(Z<-1.25)=0.1056[/tex]
