Vicente has a prism-like water tank whose base area is 1.2 square meters. He bought 6 goldfish at the store, and the store owner
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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.
<u>Given</u>:
Given that the triangle.
Let the length of the side a be 10 cm.
Let the length of the side b be 13 cm.
Let the measure of ∠C is 105°
We need to determine the area of the triangle.
<u>Area of the triangle:</u>
The area of the triangle can be determined using the formula,
Substituting a = 10, b = 13 and ∠C = 105°, we get;
Simplifying, we get;
Rounding off to 1 decimal place, we have;
Thus, the area of the triangle is 62.8 cm²