Respuesta :
Answer:
[tex]P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-5.5}{2.3})=P(z>-0.652)[/tex]
And we can find this probability with the complement rule and with the normal standard table and we got:
[tex]P(z>-0.652)=1-P(z<-0.652)= 1-0.2572= 0.7428[/tex]
Step-by-step explanation:
Let X the random variable that represent the patient recovery time of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(5.5,2.3)[/tex]
Where [tex]\mu=5.5[/tex] and [tex]\sigma=2.3[/tex]
We are interested on this probability
[tex]P(X>4)[/tex]
And we can solve this problem using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-5.5}{2.3})=P(z>-0.652)[/tex]
And we can find this probability with the complement rule and with the normal standard table and we got:
[tex]P(z>-0.652)=1-P(z<-0.652)= 1-0.2572= 0.7428[/tex]
