Answer :
Answer:
[tex] P(X >20) =0.85[/tex]
And by the complement rule we know [tex] P(X<20) =0.15[/tex]
We need to find a z score value that accumulates 0.15 of the area on the left and 0.85 of the area on the right and we got:
[tex] z = -1.036[/tex]
Since [tex] P(Z<-1.036)=0.15[/tex] and now using the z score formula we have this:
[tex] -1.03643 = \frac{20 -\mu}{0.9}[/tex]
And solving for the mean we got:
[tex] \mu = 20 + 1.03643 *0.9 = 20.93[/tex]
So the best anwer for this case would be:
e. 20.9360
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 weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,\sqrt{0.81}=0.9)[/tex]
Where [tex]\mu[/tex] the mean and [tex]\sigma=0.9[/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]
We know the following condition:
[tex] P(X >20) =0.85[/tex]
And by the complement rule we know [tex] P(X<20) =0.15[/tex]
We need to find a z score value that accumulates 0.15 of the area on the left and 0.85 of the area on the right and we got:
[tex] z = -1.036[/tex]
Since [tex] P(Z<-1.036)=0.15[/tex] and now using the z score formula we have this:
[tex] -1.03643 = \frac{20 -\mu}{0.9}[/tex]
And solving for the mean we got:
[tex] \mu = 20 + 1.03643 *0.9 = 20.93[/tex]
So the best anwer for this case would be:
e. 20.9360