eight wooden spheres with radii 3 in. are packed snugly into a square box 12 in. on one side. the remaining space is filled with
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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:
And if we solve for X we got:
And for the other case when Z=2 we have:
And if we solve for X we got:
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