APPLICATIONS OF THE NORMAL DISTRIBUTION

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Presentation transcript:

APPLICATIONS OF THE NORMAL DISTRIBUTION

EXAMPLE 1 IQ intelligence scores have a mean of 100 and a standard deviation of 15. If one person is selected at random, what is the probability he will have an IQ a) greater than 115? b) less than 95?

Example 1 – answer a First, find the z-score corresponding to the raw score of 115 Determine the shaded region. Determine proper area from chart. 1 1 Subtract from .5 because tail section: .5 - .3413 Final answer : A = .1587 or 15.87% From chart: A= .3413

Example 1 – answer b Determine the shaded region. Determine proper area from chart. -.33 Subtract from .5 because tail section: .5 - .1293 Final answer : A = .3707 or 37.07% From chart: A= .1293

Example 2 The lengths of sardines have a mean of 4.64 inches and a standard deviation of .25 inches. If the distribution is normal, what percentage of these sardines are a) shorter than 5 inches? b) from 4.4 to 4.8 inches long?

Example 2 - answer Determine the shaded region. Determine proper area from chart. 1.44 Add .5 because greater than the mean: .5 + .4251 Final answer : A = .9251 or 92.51% From chart: A= .4251

Example 2 – answer b Determine the shaded region. Determine proper area from chart. -.96 .64 Add together because on opposite sides of the mean : .2389 + .3315 Final answer : A = .5704 or 57.04% From chart: A= .2389 A= .3315

FINDING A CUT-OFF SCORE Modified z-score formula for finding a raw- score or cut-off score

Example 1: A special enrichment program in mathematics is to be offered to the top 12% of students in a school district. A standard math test given to all students has a mean of 57.3 and a standard deviation of 16. Find the cut-off score for the program.

Example 2: An exclusive college desires to accept candidates who score in the 90th percentile or above based on a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cut-off score.

Example 3: For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure. If the mean blood pressure is 120 and the standard deviation is 8, find the upper and lower readings that would qualify people to participate.