Respuesta :
Answer:
[tex]P(X>10)=P(\frac{X-\mu}{\sigma}>\frac{10-\mu}{\sigma})=P(Z>\frac{10-8.8}{2.8})=P(z>0.429)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(z>0.49)=1-P(z<0.429)=1-0.666=0.334[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the diameters of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(8.8,2.8)[/tex]
Where [tex]\mu=8.8[/tex] and [tex]\sigma=2.8[/tex]
We are interested on this probability :
[tex]P(X>10)[/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]
If we apply this formula to our probability we got this:
[tex]P(X>10)=P(\frac{X-\mu}{\sigma}>\frac{10-\mu}{\sigma})=P(Z>\frac{10-8.8}{2.8})=P(z>0.429)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(z>0.49)=1-P(z<0.429)=1-0.666=0.334[/tex]
