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And we can find this probability with thie difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
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 heights 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 with thie difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
The piece-wise function is defined as follows:
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.
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A piece-wise function is a function that has multiple definitions, depending on the input.
In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:
For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:
Goes through (3,9), hence:
b = 14.
So
For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:
Then:
When x = 10, f(x) = 10, hence:
10 = 15 + b
b = -5.
Hence:
More can be learned about piece-wise functions at brainly.com/question/24734454
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The triangles are similar triangles, and the values of HK and GH are (b) 4 and 2√5, respectively
<h3>How to determine the length HK?</h3>The triangles are similar triangles, and they are represented by the following similarity ratio:
GK : HK = HK : JK
From the question, we have:
GK = 2 and JK = 8
So, we have:
2 : HK = HK : 8
Express as fractions
Cross multiply
HK² = 16
Take the positive square root of both sides
HK = 4
The length GH is calculated using the following Pythagoras theorem
GH² = GK² + HK²
This gives
GH² = 2² + 4²
Evaluate the squares
GH² = 20
Solve for GH
GH = 2√5
Hence, the values of HK and GH are (b) 4 and 2√5, respectively
Read more about similar triangles at:
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