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The invNorm(area, m, s) function on the TI calculator is often used to compute the critical z-score associated with a  given cumulative probability distribution (area). It is also often used to compute the actual raw score  associated with the area of a cumulative probability distribution when the mean and standard deviation are given.

invNorm(area, m, s) Function Parameters

Area: a specified area (cumulative probability distribution). The value must be between 0 and 1.

Mean: The mean  of the data under question.

Standard Deviation: The standard deviation of the data under question.


Example 1:  Find the critical z value for a confidence level of 95 percent (significance level of 5 percent) for a right tail test.

Solution: Enter 0.95 for the area in the invNorm function

InvNorm(0.95)

which returns an associated z-critical value of 1.645 standard deviations


Example 2: What must be the minimum z-score obtained to pass a college entrance exam if only the top 10 percent of the scores are accepted. the mean score on the test is 740 and the standard deviation is 40.

Solution: Since only the highest 10 percent of scores will pass, the area under the normal distribution curve is 1 – 0.1 = 0.9. Substituting 0.9  for the area, 740 for the mean and 40 for the standard deviation into the TI-83/84/89 calculator’s invNorm function

InvNorm(0.9, 740, 40)

Returns a value of  791.3

So the minimum raw data score needed  to be accepted would be 791.3. This implies that a 90 percentile ranking for this test is  about 1.28 standard deviations above the mean. This is exactly what you would obtain if you calculated just the critical z-score using the invNorm function, e.g.

invNorm(0.9) = 1.28

About BookMark Tutoring

BookMark Tutoring provides statistics tutoring for students in Elementary Statistics 15 at Santa Rosa Junior College as well as statistics courses offered at Sonoma State University.