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Answer:
1.
2.
3.
Step-by-step explanation:
Assuming the value for the mean 79 and the deviation 8.8
1) 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".
2) Part a
Let X the random variable that represent the amount of collagen of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
3) Part b
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
4) Part c
We need to find first the limits for 3 deviations within the mean
And we can find this probability on this way:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.