10/17/22, 12:22 AM Standard Normal Table (Page 2) POSITIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .02 .03 .05 06 .07 08 09 .01 .04 5359 0.0 .5000 5040 -5080 5120 5160 .5199 .5239 5279 5319 5753 0.1 .5398 5438 5478 5517 .5557 .5596 .5636 5675 5714 6103 6141 0.2 5793 ,5832 5871 5910 .5948 .5987 .6026 606 0.3 .6179 6217 6255 6293 633 6368 .6406 6443 6480 6517 5844 6879 0.4 6554 .6591 6628 566 6700 6736 5772 6808 0.5 .6915 .6950 6985 7019 .7054 7088 7123 7157 7190 7224 0.6 .7257 .7291 7324 7357 7389 7422 .7454 .7486 7517 7549 0.7 .7580 7611 7642 7673 770 7734 .7764 779 7823 7852 8106 8133 0.8 .7881 .7910 7939 7967 7995 8023 .8051 8078 0.9 .8159 .8186 8212 8238 8264 8289 8315 8340 8365 8389 .8413 846 8485 850 .8531 8554 .8577 8599 .8621 1.0 8438 1.1 .8643 .8665 8686 8708 372 8749 8770 ,8790 8810 8830 8925 .8944 8962 ,8980 ,8997 9015 1.2 .8849 8869 8868 890 1.3 9032 9045 .9066 9082 9099 .9115 .9131 .9147 9162 9177 1.4 9207 9222 9236 9251 9265 .9279 9292 9306 9319 9192 1.5 9370 9382 9394 .940 9418 9429 9441 .9332 9345 9357 1.6 9452 .9463 94/4 9484 9495 .9505 .9515 9525 9535 9545 1.7 .9554 9564 9573 9582 9591 9599 .9608 9616 9625 9633 9706 1.8 .9641 9649 .9656 9664 9671 9678 9686 9693 9699 9767 1.9 .9713 .9719 9726 9732 9738 9744 9750 9756 9761 9808 9812 981 2.0 9772 9778 9783 9788 9793 9798 9803 .9821 .9826 9830 983 383 9842 9846 9854 2.1 9850 985 2.2 .9861 .9864 9868 9871 9875 9878 9881 9884 9887 9890 2.3 .9893 9896 9898 990 9904 9906 9909 .9911 9913 9916 .9936 2.4 9918 .9920 9922 9925 9927 .9929 .9931 9932 9934 2.5 9938 .9940 9941 9943 9945 9946 9948 9949 9951 9952 .9955 ,9956 9957 9959 9960 9961 9962 9963 9964 2.6 .9953 9972 9973 9974 2.7 9965 .9966 9967 9968 9969 970 2.8 .9974 9975 9976 9977 9977 9978 9979 9979 9980 9981 2.9 .9981 9982 9982 9983 9984 9984 9985 9985 9986 9986 9990 9990 3.0 9987 9987 9987 9988 9988 9989 9989 998 9992 9992 3.1 9990 .9991 9991 999 9992 9992 9993 9993 9995 999 3.2 9993 .9993 9994 9994 9994 .9994 9994 9995 9997 3.3 .9995 9995 9995 9996 9996 9996 9996 999 9996 3.4 .9997 .9997 9997 999 9997 .9997 .9997 .9997 9997 9998 5.50 .9999 and up VOTE: For values of z above 3.49, use 0.9999 for the area. Common Critical Value Use these common values that result from interpolation: Confidence | Critical Level Value z score Area 0.90 1,645 1.645 0.9500 0.95 1.96 2.575 0.9950 0.99 2.575 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170668&questionId=15&flushed=false&cld=6988267¢erwin=yes 1/110/17/22, 12:22 AM Standard Normal Table (Page 1) NEGATIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.50 and lower .0001 -3.4 0003 .0003 .0003 .0003 0003 .0003 .0003 0003 .0003 .0002 -3.3 0005 0005 0004 0004 .000 0004 0004 OOO 0003 -3.2 0007 0007 0006 0006 0006 0006 0006 0005 000 0005 -3.1 1010 0009 .0009 0009 0008 .0008 0008 0008 0007 0007 -3.0 013 .0013 .0013 0012 0012 .0011 0on1 0011 .0010 0010 -2.9 0019 0018 0018 0017 0016 .0016 0015 .0015 0014 0014 2.8 .0026 0025 0024 0023 0023 002 0021 0021 0020 0019 27 0035 0034 .0033 0032 0031 .0030 002 0028 .0027 .0026 -2.6 .0047 0045 0044 0043 0041 0040 0039 0038 .0037 0036 2.5 .0062 0060 005 0057 .0055 0054 0052 .0051 .0049 0048 2.4 0082 0080 0078 0075 0073 .0071 .0069 0068 .0066 .0064 0107 0104 0102 0099 0096 .0094 009 0089 0087 0084 0139 0136 .0132 0129 0125 0122 0119 0116 .0113 0110 .0179 0174 .0170 0166 0162 .0158 0154 0150 .0146 .0143 -2.0 .0228 .0222 0217 0212 0207 .0202 0197 0192 .0188 0183 -19 0287 0281 .0274 0268 0262 0256 250 0244 0239 0233 -18 0359 .0351 .0344 0336 0329 .0322 .0314 0307 .0301 .0294 0446 0436 0427 0418 0409 0401 0392 0384 0375 0367 1.6 .0548 .0537 .0526 0516 0505 .0495 048 0475 .0465 045 .0668 .0655 0643 0630 0618 .0606 0594 .0582 0571 0559 0808 0793 0778 0764 0749 0735 .0721 0708 0694 0681 -1.3 0968 0951 0934 0918 0901 088 086 0853 .0838 0823 -12 .1151 1131 1712 1093 1075 1056 1038 1020 1003 0985 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 287 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 .4641 NOTE: For values of z below -3.49, use 0.0001 for the area. "Use these common values that result from interpolation: z score Area -1.645 0.0500 -2.575 0.0050 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627170668&questionId=15&flushed=false&cld=6988267¢erwin=yes 1/1A survey found that women's heights are normally distributed with mean 62.7 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 69.3 in. and standard deviation 3.2 in. Consider an executive jet that seats six with a doonNay height of 56.4 in. Complete parts (a) through (0) below. (E a. What percentage of adult men can t through the door without bending? The percentage of men who can fit without bending is |:|%. (Round to two decimal places as needed.) A survey found that women's heights are normally distributed with mean 63.5 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. lfthis branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements? Click to View page 1 of the table. Click to View page 2 of the table. Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of u = 24.6 in. and a standard deviation of o = 1.2 in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) $ 0.01 and a value is significantly low if P(x or less) $ 0.01. Find the back-to-knee lengths separating significant values from those that are not significant. Using these criteria, is a back-to-knee length of 26.9 in. significantly high? . . Find the back-to-knee lengths separating significant values from those that are not significant. Back-to-knee lengths greater than in. and less than in. are not significant, and values outside that range are considered significant. (Round to one decimal place as needed.)Assume that adults have IQ scores that are normally distributed with a mean of 95.2 and a standard deviation 23.4. Find the rst quartile Q1 , which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.) E} The first quartile is E. (Type an integer or decimal rounded to one decimal place as needed.) Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 0.8 in. Find P90. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%. E) The hip breadth for men that separates the smallest 90% from the largest 10% is P90 = D in. (Round to one decimal place as needed.) Assume that adults have IQ scores that are normally distributed with a mean of p: 100 and a standard deviation 5 = 20. Find the probability that a randomly selected adult has an IQ between 82 and 118. Click to View [age 1 of the table. Click to View p_age 2 of the table. E) The probability that a randomly selected adult has an IQ between 82 and 118 is El. (Type an integer or decimal rounded to four decimal places as needed.) Assume that adults have IQ scores that are normally distributed with a mean of 101 and a standard deviation of 20.1. Find the probability that a randomly selected adult has an IQ greater than 123.6. (Hint: Draw a graph.) E) The probability that a randomly selected adult from this group has an IQ greater than 123.6 is D. (Round to four decimal places as needed.) Assume that adults have IQ scores that are normally distributed with a mean of p = 100 and a standard deviation 0 =15. Find the probability that a randomly selected adult has an IQ less than 121. Click to View [5199 1 of the table. Click to View p_age 2 of the table. CE The probability that a randomly selected adult has an IQ less than 121 is E. (Type an integer or decimal rounded to four decimal places as needed.) Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 0.1151 9,9 The indicated IQ score is D. (Round to the nearest whole number as needed.) Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and + those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. 0.75 X . . . The indicated IQ score, x, is (Round to one decimal place as needed.)