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Answer:
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".
Let X the random variable that represent the Shear strength of a population, and for this case we know the distribution for X is given by:
Where and
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
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:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
4x² + 9x - 1 = 0
<u>Step 2: Define variables</u>
a = 4
b = 9
c = -1
<u>Step 3: Find roots</u>
- Substitute:
- Exponents:
- Multiply:
- Subtract: