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Middle on the Normal distribution

Middle on the Normal distribution. Z. -1.28 0 1.28. .1003. .8997. .8997 - .1003 = .7994. 1 - .8997 = .1003.

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Middle on the Normal distribution

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  1. Middle on the Normal distribution

  2. Z -1.28 0 1.28 .1003 .8997 .8997 - .1003 = .7994 1 - .8997 = .1003 What is going on here? It is just an exercise in using the Z table and finding the middle .8000 , or middle 80% of values. Note, with the middle .8000, .2000 is left and half is on each side. From a practical point of view, from the table -1.28 has .1003 in the low tail. This is more than the .1000, but is the closest in the table. Z = 1.28 means we would have .1003 in the upper tail. Thus between Z’s -1.28 and 1.28 we have the middle .8000.

  3. Z -1.645 0 1.645 .0500 .9500 .9500 - .0500 = .9000 1 - .9500 = .0500 What is going on here? It is just an exercise in using the Z table and finding the middle .9000 , or middle 90% of values. Note, with the middle .9000, .1000 is left and half is on each side. From a practical point of view, from the table -1.645 has .0500 in the low tail. The tradition here is to go in the middle of -1.64 and -1.65. Z = 1.645 means we would have .0500 in the upper tail. Thus between Z’s -1.645 and 1.645 we have the middle .9000.

  4. Z -1.96 0 1.96 .0250 .9750 .9750 - .0250 = .9500 1 - .9750 = .0250 What is going on here? It is just an exercise in using the Z table and finding the middle .9500 , or middle 95% of values. Note, with the middle .9500, .0500 is left and half is on each side. From the table -1.96 has .0250 in the low tail. Z = 1.96 means we would have .0250 in the upper tail. Thus between Z’s -1.96 and 1.96 we have the middle .9500.

  5. Problem 18 page 219 π = .77 and thus the standard error = sqrt((.77)(.23)/200)) = .03 when rounding. a. The Z for .75 is (.75 - .77)/.03 = -.67 and the Z for .80 is (.80 - .77)/.03 = 1.00. Thus we have .8413 - .2514 = .5899 b. Remember the middle uses Z’s of -1.645 and 1.645 Thus the lower sample percentage is found by solving for p in the formula (really just the Z score formula applied to proportions) -1.645 = (p - .77)/.03 or p = -1.645(.03) + .77 = .72065 and on the high end 1.645 = (p - .77)/.03 or p = 1.645(.03) + .77 = .81935. c. The Z’s here are -1.96 and 1.96 so we get .77 + and - .0588. So on the low side we have .7112 and on the high side we have .8288

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