Respuesta :
Answer:
[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]
And using the normal standard distribution or excel we got:
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]
Step-by-step explanation:
Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(24,3)[/tex]
Where [tex]\mu=24[/tex] and [tex]\sigma=3[/tex]
We want to find this probability:
[tex]P(21<X<28)[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]
And using the normal standard distribution or excel we got:
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]
