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#### The Normal Distribution Finding Area We looked at three types of examples, finding the left area, right area, and between area. In any case, we have to look up the table to find the left cumulative area that corresponds to z-scores.   Please keep in mind that our z-table always gives the left cumulative area. For finding the left area of...

#### Probability by Tree Method A probability tree is a simple and effective method of applying the probability rules by representing events in an experiment by lines.  It is shown as two levels and two branches.

#### The Normal Distribution Finding z scores In summary, we use the left cumulative area to find z-scores.  If the right area is given, then subtract the right area from 1 to look up the table.

#### Constructing a box plot To draw a box-plot, we need five measurements, the minimum, Q1, Q2, Q3, and the maximum. First of all, we need to rearrange the data set, find a position of Q1, Q2, and Q3 by the formula, and then find the actual value on each position.  Those values are Q1, Q2, and Q3. Thank you...

#### Logarithmic Differentiation This method allows us to differentiate very complicated fractional functions or functions raised to the power of another function easily.

#### Integration by Simple u substitution #### Graphing by Hand

Here are tips for graphing. First, you need to find x-intercepts and y-intercept, if possible.  For x-intercepts, setting y=0 to find x-values and similarly, setting x=0 to find y-intercept. Then, investigate if there are any asymptotes for fractional functions. For the horizontal asymptotes, we need to take the limit at infinity.  If you get the...

#### Limits At Infinity To evaluate the limit as x approaches infinity, take the largest exponent term each  from the numerator and denominator, simplify the fraction, and then apply the limit rules as shown.

#### Integrating by Trigonometric Substitution This method allows us to change algebraic functions into trigonometric functions, integrate them in trigonometric forms, and return to the original algebraic functions as solutions.

#### Solving Differential Equation by Laplace Transforms Before starting the example, you need to know the following steps to solve DE by Laplace transforms. Step 1.  Take the Laplace transforms of both sides of the equation. Step 2. Solve for the Laplace of Y. Step 3. Manipulate the Laplace transform, F(s) until it matches one or more table entries. Step 4. Take...
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