example: What proportion of the area under a normal curve lies to the left of z = –1.37?
solution: There are two ways to do this problem, and you should be able to do it either way.
(i) The first way is to use the table of Standard Normal Probabilities. To read the table, move down
the left column (titled “z ”) until you come to the row whose entry is –1.3. The third digit, the 0.07
part, is found by reading across the top row until you come to the column whose entry is 0.07. The
entry at the intersection of the row containing –1.3 and the column containing 0.07 is the area
under the curve to the left of z = –1.37. That value is 0.0853.
(ii) The second way is to use your calculator. It is the more accurate and more efficient way. In the
DISTR menu, the second entry is normalcdf (see the next Calculator Tip for a full explanation of
the normalpdf and normalcdf functions). The calculator syntax for a standard normal
distribution is normalcdf (lower bound, upper bound) . In this example, the lower bound can be
any large negative number, say –100.normalcdf(-100,-1.37)= 0.0853435081 .Calculator Tip: Part (ii) of the previous example explained how to use normalcdf for standard
normal probabilities. If you are given a nonstandard normal distribution, the full syntax is
normalcdf(lower bound, upper bound, mean, standard deviation) . If only the first two parameters
are given, the calculator assumes a standard normal distribution (that is, μ = 0 and σ = 1). You will
note that there is also a normalpdf function, but it really doesn’t do much for you in this course.
Normalpdf(X) returns the y -value on the normal curve. You are almost always interested in the area
under the curve and between two points on the number line, so normalcdf is what you will use a lot in
this course.
For older versions of the TI-8s/84 calculators, it can be difficult to remember the parameters that
go with the various functions on your calculator—knowing, for example, that for normalcdf , you put
lower bound, upper bound, mean, standard deviation in the parentheses. The APP “CtlgHelp” can
remember for you. It comes on the older versions of the TI-83/84 and is activated by choosing
CtlgHelp from the APPS menu and pressing ENTER twice. Newer versions have menus with prompts,
making this APP unnecessary.
To use CtlgHelp , move the cursor to the desired function on the DISTR menu and press +. The
function syntax will be displayed. Then press ENTER to use the function on the home screen. Note that,
at this writing, CtlgHelp does not work for invT or χ^2 gof. The following is a screen capture of using
CtlgHelp that displays the parameters for normalcdf: