3)Find the PROBABILITY of data being to the LEFT or these standard deviations (z-values) from the mean:
Probability to Probability to +z- value Probability to Probability to LEFT RIGHT LEFT Right CIRCLE THE PROBABILITIES TO THE LEFT [not "Right\" on a copy of the Tables after writing them' In the boxes above. You can use one copy of each Table to "find and circle", just label them 4a, 4b, etc. 4) How many standard deviations to the LEFT (zvalue} correspond to these probabilities (3} 0.0329 2; {[3} 0.0007 ; (c) 0.3859 5} How many standard deviations to the RIGHT (+zvalue] correspond to these probabilities [to the left) (3} 0.9995 2; {[3} 0.9864 ; (c) 0.6103 QQTrickier} What number of standard deviations { zvalue] corresponds to these percentages (probabilities) of data being ABOVE (to the right) (a}0.119 i- 000.0495 ; 090.409 7} How do you go back to the original data set to find an. xvalue if you are given the zvalue (and the mean and standard deviation of the that original data set? Remember the conversion formula 2 = [x mean} I std dev ? Can you dust off your algebra and solve this equation for II? It = ??? [SHOW FORMULA 8:. SET UPS] a] NOW, use this version of the formula to nd the II data value corresponding to a z-value of -1.65 from a data set that has a mean of 15 and SD of 6. b] z-value = -2.48 data set mean = 25 and SD = 3 c} z-value = +2.09 data set mean = 52 and SD = 16 gzl'Data made up} x = blood pressure of a person in Maryland (measured in mm Hg (Hg = mercury\" We MUST assume these blood pressures have a NORMAL Distribution. We KNOW the true Population mean pressure is 125 mm Hg \".1 = 125) and Population std dev {SD} is 20 mm Hg lo = 20), which means we don't need to rely on sample data. (a) Probability a blood pressure is greater than or equal to 140 mm Hg=[P[x} 2 140 mm Hg} (note: capital P] 1} Standardize x = 140 to get the z-value which represents many standard deviations this xvalue is from the mean using 2 = {x- meanlfSD z = 2} Depending on whether this z-value is positive or negative go to the appropriate z-Table and nd the probability [area to the LEFT) that this z-number of standard deviations represents: NOTE: IF it's an x is GREATER THAN groblem [like this one) we want the area [probability] to the RIG HT. But z-values always give areas to the left, so once we have the probability corresponding to a calculated 2- value, we SUBTRACT that probability from 1.00 or 100% to get the probability to the right (the x is greater than probability] But, if it's an x is LESS THAN problem, we simply get that probability directly from our z-value and the 2- Table. 3] From the z-Table we now know the probability to the LEFT (which would represent the probability of I being LESS than 140% we need to subtract that probability from 100% or 1.000 to get the probability to the RIGHT [I being greater than 140). That probability is: [b] Probability a blood pressure is LESS THAN 150 mm Hg:{ Phi] E 150 mm Hg) 1: = 150 Follow same steps as with [a] and read the NOTE. (c) Probability blood pressure is between 115 and 130 mm HG Need to calculate TWO probabilities: x 265 ? z-value: ; Probability: [this is the probability (area) to the LEFI', is that what you want here? If gt what is the correct probability? jHow did you calculate it?) (c) REPEAT [a] and lb) IF the sample size {n} is 40 instead of 11. 1What did you use as the mean: ,what did you use for the new population SD: g: 265}: z = , Probability: (left or right?} UNusual at 5% level? NEGATIVE Z-VALUES (Standard Deviations below the mean) NEGATIVE Z-VALUES Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 04 05 .06 .07 .08 .09 -3.50 and lower 000 -3.4 0003 0003 0003 0003 0003 0003 0003 0003 0003 0002 -3.3 0005 0005 0005 0004 0004 0004 0004 0004 0004 0003 -3.2 0007 0007 0006 0006 0006 0006 0006 0005 0005 0005 -3.1 .0010 .0009 0009 0009 .0008 0008 0008 0007 0007 -3.0 0013 0013 0013 0012 0012 0011 0011 .0011 0010 0010 -2.9 .0019 0018 0018 0017 0016 0016 0015 0015 0014 0014 -2.8 0026 0025 0024 0023 0023 0022 0021 0021 0020 0019 -2.7 .0035 0034 0033 0032 003 0030 0029 0028 0027 0026 -2.6 0047 0045 0044 0043 0041 0040 0039 0038 0037 0036 -2.5 0062 0060 0059 0057 0055 0054 0052 0051 * .0049 0048 -2.4 0082 0078 0075 0073 007 0069 0068 A .0066 0064 -23 0107 D104 0102 0099 0096 0094 009 0089 .0087 0084 -22 0139 0136 0132 0129 0125 0122 0119 0113 0110 -21 0179 0174 0170 0166 0162 015 0154 0150 .0146 0143 -2.0 0228 0222 0217 0212 0207 0202 0197 .0192 0188 0183 -1.9 0287 0281 0274 0268 0262 0256 0250 0244 .0239 0233 -1.8 0359 0351 0344 0336 0329 0322 0314 0307 0301 0294 -17 0446 0436 0427 .0418 0409 0401 0392 0384 .0375 0367 -1.6 0548 0537 0526 .0516 0505 *.0495 0485 0475 0465 0455 -1.5 0668 0655 0643 .0630 .0618 A .0606 0594 0582 0571 0559 -1.4 0808 0793 0778 0764 0749 0735 0721 0708 0694 0681 -1.3 .0968 .0951 .0934 0918 .0901 0885 0869 0853 0838 0823 -1.2 .1151 .1131 .1112 1093 1075 1056 1038 1020 1003 0985 -1.1 1357 1335 1314 1292 1271 .1251 1230 .1210 .1190 1170 -1.0 1587 1562 1539 1515 .1492 1469 1446 1423 1401 1379 -0.9 1841 1814 1788 1762 1736 .1711 1685 1660 1635 1611 -0.8 2119 2090 2061 2033 2005 1977 1949 1922 1894 1867 -0.7 .2420 2389 2358 2327 .2296 2266 2236 2206 2177 2148 -0.6 2743 2709 2676 2643 2611 2578 2546 2514 2483 2451 -0.5 3085 3050 .3015 2981 .2946 2912 2877 2843 2810 2776 -0.4 3446 3409 3372 .3336 3300 3264 3228 3192 3156 3121 -0.3 3821 3783 3745 3707 3669 3632 3594 .3557 .3520 3483 -0.2 4207 4168 4129 4090 4052 4013 3974 3936 .3897 3859 -0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 -0.0 5000 4960 4920 .4880 .4840 4801 4761 4721 .4681 4641POSITIVE Z-VALU ES [standard Deviations ABOVE the mean] Cumulative Area from the LEFT .04 .05 .05 .0? .09 .09 .5150 .5199 .5239 .5239 .5319 .5948 .598? 45095 5954 .7422 .9454 .485_' .751? .9549 .9995 .9025 5051 .8918 .8105 .8155 m 9655 4621 .8925 5944 9255 .91 .925 .9219 .9484 .9495 t .9595
