Respuesta :
Answer:
[tex]P(5.5<X<6)=P(\frac{5.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{6-\mu}{\sigma})=P(\frac{5.5-5.75}{0.11}<Z<\frac{6-5.75}{0.11})=P(-2.27<z<2.27)[/tex]
And we can find this probability with this difference:
[tex]P(-2.27<z<2.27)=P(z<2.27)-P(z<-2.27)=0.988 -0.0116=0.9764[/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(5.75,0.11)[/tex]
Where [tex]\mu=5.75[/tex] and [tex]\sigma=0.11[/tex]
We are interested on this probability
[tex]P(5.5<X<6)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(5.5<X<6)=P(\frac{5.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{6-\mu}{\sigma})=P(\frac{5.5-5.75}{0.11}<Z<\frac{6-5.75}{0.11})=P(-2.27<z<2.27)[/tex]
And we can find this probability with this difference:
[tex]P(-2.27<z<2.27)=P(z<2.27)-P(z<-2.27)=0.988 -0.0116=0.9764 [/tex]
