With a few little improvements and extras by D.R.S, University of Cordele. Section 6.2. Finding Area under a Normal Distribution IMPORTANT: “Area” is “_____________” IMPORTANT: “Probability” is “_________”. - PowerPoint PPT Presentation
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Example 6.4 : Finding Area to the Right of a Positive z-Value Using a Cumulative Normal Table
Find the area under the standard normal curve to the right of z = 1.37. Table Method: Total area under curve is _______, Use Subtraction: Total area ________ Minus area to the left of z = 1.37, which is ________ Equals area to the right of z = 1.37, which is ________
TI-84 Method: normalcdf(left endpoint, right endpoint)normalcdf(1.37, 1E99); the result is _______________
Example 6.4 : Finding Area to the Right of a Positive z-Value Using a Cumulative Normal Table (cont.)
• Alternative Table Method: Because of symmetry, the area to the right of z = 1.37 is the same asthe area to the _______ of z = ________z 0.09 0.08 0.07 0.06 0.05
Example 6.5: Finding Area to the Right of a Negative z Value Using a Table or a TI-83/84 Plus Calculator (cont.)
Excel: Area to the right of z = -0.90
=1-NORM.S.DIST(z value, TRUE)Like the printed table, NORM.S.DIST only gives you area to the left. It doesn’t do area “between” two z values like the TI-84’s normalcdf() does.So the “1 minus area to the left” technique is needed.
Example 6.6: Finding Area between Two z-Values Using Tables or a TI-83/84 Plus Calculator
Find the area under the standard normal curve between z1 = -1.68 and z2 = 2.00.
Table Method:Area to the left of z = _______ is ________Area to the left of z = _______ is ________Subtract: _______ - _______ = ________TI-84 Method:normalcdf ( _____, _____) = _________________
Example 6.6: Finding Area between Two z-Values Using Tables or a TI-83/84 Plus Calculator (cont.)
Area to the left minus equalsof the area to the left the arearight endpoint of the between left endpoint the two endpoints
Excel: Area between z = -1.68 and z=2.00
=NORM.S.DIST(high z,TRUE)-NORM.S.DIST(low z, TRUE)Like the printed table, NORM.S.DIST only gives you area to the left. It doesn’t do area “between” two z values like the TI-84’s normalcdf() does.So the subtraction of two areas technique is needed.
Example 6.8: Finding Area in the Tails for Two z-Values Using a TI-83/84 Plus Calculator (cont.)
Note an alternative method for finding this area that is particularly clever. By definition, we know that the total area under the curve equals 1. Using this fact, the area in the tails can be obtained by finding the area between z1 = −2.50 and z2 = 3.00 and then subtracting that area from 1.
Example 6.11 : Finding Probabilities for the Standard Normal Distribution Using Tables or a TI 83/84 Plus Calculator ‑
Find the following probabilities using the cumulative normal distribution tables or a TI-83/84 Plus calculator.Write details and draw sketches. a. P(z < 1.45) b. P(z −1.37)
Example 6.11 : Finding Probabilities for the Standard Normal Distribution Using Tables or a TI 83/84 Plus Calculator ‑
Find the following probabilities using the cumulative normal distribution tables or a TI-83/84 Plus calculator.Write details and draw sketches. c. P(1.25 < z < 2.31) d. P(z < −2.5 or z > 2.5)