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The Density Curve for a Continuous Random Variable Is Shown P(x<1)P ( x < 1 )

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The density curve for a continuous random variable is shown below. Use this curve
to find the following probabilities:  The density curve for a continuous random variable is shown below. Use this curve to find the following probabilities:   a)  P ( x < 1 )  b) P ( 2 < x < 4 )   You may need to use the following area formulas in your calculations: Area of a rectangle:  A = l w  Area of a trapezoid:  A = \frac { 1 } { 2 } h \left( b _ { 1 } + b _ { 2 } \right)  Area of a right triangle:  A = \frac { 1 } { 2 } a b
a) P(x<1)P ( x < 1 )
b) P ( 2 < x < 4 )


You may need to use the following area formulas in your calculations:
Area of a rectangle: A=lwA = l w
Area of a trapezoid: A=12h(b1+b2)A = \frac { 1 } { 2 } h \left( b _ { 1 } + b _ { 2 } \right)
Area of a right triangle: A=12abA = \frac { 1 } { 2 } a b

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Definitions:

Marginal Tax Rate

The rate at which the next dollar of taxable income is taxed, indicating how much of an additional dollar earned will be taken in taxes.

Taxable Income

The sum of money earned by a person or a business that is used to calculate the owed tax payable to the government.

After-Tax Income

The amount of income that remains after all taxes have been deducted.

Sales Tax

A tax levied by a government on the sale of goods and services, typically calculated as a percentage of the selling price.

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