Use calculator to find the value of z* that yields the probability shown. 1. P(Z2*)=0.0055 | 2.5427 4. P(Z>z*)=0.7995 ~0.8398 Answer 1: -0.4399 Answer 2: 2.3301 Answer 3: 2.5427 Answer 4: -0.8398 Incorrect Question 2 Find the value of &* that yields the probability shown, where X is a normally distributed random variable X with mean 54 and standard deviation 12. 1. P(Xz*)=0.6500 49-38 Answer 1: 37.91 Answer 2: 49.38 Incorrect Question 3 Heights of women are normally distributed with mean 63.7 inches and standard deviation 2.47 inches. 1. Find the height that is the 10th percentile. 60.53 2. Find the height that is the 80th percentile. 65.78 Answer 1: 60.53 Answer 2: 65.78 The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds. 1. The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.) 297 . In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf) 1.87 Answer 1: 297 Answer 2: 1.87 \f* * = 2. 6 + M = (-0. 39 ) . 12 + 54 X -49. 38\f\f\f\fSTANDARD NORMAL DISTRIBUTION Z Score Table 0.0 | .50000 50399 .50798 51197 51595 .51994 52392 52790 .53188 .53586 0.1 | 53983 54380 54776 55172 55567 .55962 56356 56749 57142 57535 0.2 | 57926 38317 58706 59095 59483 .59871 60257 60642 61026 .61409 0.3 | 61791 62172 62552 62930 .63307 .63683 .64058 64431 64803 65173 0.4 | 65542 65910 66276 .66640 67003 67364 67724 68082 68439 68793 0.5 [ 69146 69497 69847 70194 70540 70884 71226 71566 71904 .72240 0.6 | .72575 .72907 .73237 .73565 .73891 .74215 .74537 74857 75175 75490 0.7 | .75804 76115 76424 76730 77035 .77337 .77637 .77935 .78230 .78524 0.8 | .78814 .79103 .79389 .79673 .79955 .80234 80511 80785 .81057 .81327 0.9 | 81594 81859 .82121 .82381 82639 .82894 83147 83398 .83646 .83891 1.0 | 84134 84375 84614 84849 85083 85314 85543 85769 .85993 .86214 1.1 | 86433 86650 .86864 87076 .87286 .87493 .87698 .87900 .88100 .88298 1.2 | 88493 88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 13| 90320 90490 90658 90824 90988 .91149 91309 91466 91621 91774 1.4 ] 91924 92073 92220 92364 92507 92647 92785 92922 93056 .93189 - Negative Z Score Table Positive Z Score Table