Answer:
If the weight is higher than 5.8886 gr would be considered significantly high
If the weight is lower than 5.6121 gr would be considered significantly low
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:
Where
and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
For the case when z =-2 we can do this:
![-2 = \frac{X-5.75241}{0.06281}](https://tex.z-dn.net/?f=%20-2%20%3D%20%5Cfrac%7BX-5.75241%7D%7B0.06281%7D)
And if we solve for X we got:
![X = 5.75241 -2*0.06281 =5.6121](https://tex.z-dn.net/?f=%20X%20%3D%205.75241%20-2%2A0.06281%20%3D5.6121)
And for the other case when Z=2 we have:
![2 = \frac{X-5.75241}{0.06281}](https://tex.z-dn.net/?f=%202%20%3D%20%5Cfrac%7BX-5.75241%7D%7B0.06281%7D)
And if we solve for X we got:
![X = 5.75241 +2*0.06281 =5.8886](https://tex.z-dn.net/?f=%20X%20%3D%205.75241%20%2B2%2A0.06281%20%3D5.8886)
If the weight is higher than 5.8886 gr would be considered significantly high
If the weight is lower than 5.6121 gr would be considered significantly low