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Calculating Areas under the Normal Curve

The TI-83 calculator  may be used to compute $P(a \leq X \leq b)$, or the area under the normal curve between a and b. You will need to input the two boundary numbers a and b, and the center and spread of the curve (called the mean and SD of the curve, respectively). See Figure  4.3.


  
Figure: Area under normal curve between a and b [ $P(a \leq X \leq b)$]
\begin{figure}
\begin{center}
\epsfig{file=annieNormshaded_ab.ps, width=4.5in, angle=-90}\end{center}\end{figure}

\fbox{ \parbox{5.5in}{
\vspace*{1ex}
{\bf Using the TI-83:} Calculating $P(a \le...
...
\hspace*{4em}with a parenthesis.\\
\hspace*{2em}4. [ENTER]
\vspace*{1ex}
} }

Example: Returning to our sales problem, the mean is 36 and the SD is 8. We need the area to the right of 40, or the area under the curve between a=40 and $b=\infty$. (In place of $b=\infty$, you may type any number that is 5 or more SD's above the mean, since there is negligible area beyond 5 SD's on either side). Now, 5 SD's above the mean is 36+5(8)=76, so using a convenient value like b=9999 is appropriate. Typing the inputs (40, 9999, 36, 8) to [NORMALCDF] will give you the desired area $P(a \leq X \leq b)= .3085$, or approximately 31%.

Exercise: Examine the idealized stem-and-leaf in Figure  4.2.
a. What percentage of the data is larger than 40 (exclusive, i.e. excluding 40)?
b. What percentage of the data is larger than 40 (inclusive)?
c. If we split the difference between inclusive and exclusive, what percentage
of the data is larger than 40? Is this close to 31%?


next up previous contents index
Next: Calculating Percentiles Using the Up: Computing Probabilities Using the Previous: Computing Probabilities Using the

2003-09-08