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 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. -1.645 0 1.645.0500.9500.9500 -.0500 =.9000 1 -.9500 =.0500

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