Respuesta :
Answer:
[tex]P(18<X<22)=P(\frac{18-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{22-\mu}{\sigma})=P(\frac{18-20}{2}<Z<\frac{22-20}{2})=P(-1<z<1)[/tex]
And we can find this probability with the normal standard distribution and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841 -0.159= 0.682[/tex]
Step-by-step explanation:
Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(20,2)[/tex]
Where [tex]\mu=20[/tex] and [tex]\sigma=2[/tex]
We are interested on this probability
[tex]P(18<X<22)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(18<X<22)=P(\frac{18-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{22-\mu}{\sigma})=P(\frac{18-20}{2}<Z<\frac{22-20}{2})=P(-1<z<1)[/tex]
And we can find this probability with the normal standard distribution and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841 -0.159= 0.682[/tex]
