Question
Asked Oct 15, 2019
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A sample of 36 children with low self-esteem is given a standardized test for depression. Find the probability that an average depression score to be more than 97 out of a sample of 36? Graph the distribution and label at least  three standard deviation above and below the mean. Shade the distribution according to the question?

The mean is 90 and the standard deviation is 12, i'm not sure if I have to work out a new standard deviation?

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Expert Answer

Step 1

Given sample size n = 36
Mean = 90
Standard deviation = 12

The standard deviation of the sample is   σ/√n and the formula to calculate the Z score is given below. By substituting values we get the Z score for score 97 is 3.5.

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X- Z = 97-90 7 Z= 3.5 12/6 12 36

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Step 2

With reference to Z table the probability to right of Z score 3.5 is 0.0011.
The probabilit...

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0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.4681 0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4641 0.4325 0.4286 0.4247 0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4207 0.4052 03936 0.2 0.4168 0.4129 0.4090 0.4013 0.3974 0.3897 0.3859 0.3707 0.3632 0.3 0.3821 03783 0.3745 0.3669 0.3594 0.3557 0.3520 03483 0.3372 0.4 03446 0.3409 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.2946 0.2810 0.5 03085 0.3050 0.3015 0.2981 0.2912 0.2877 0.2843 0.2776 0.2743 0.2611 0.6 0.2709 0.2676 0.2643 0.2578 0.2546 0.2514 0.2483 0.2451 0.2177 0.7 02420 0.2389 0.2358 0.2327 02296 0.2266 0.2236 0.2206 0.2148 0.2033 0.1894 0.8 0.2119 0.2090 0.2061 0.2005 0.1977 0.1949 0.1922 0.1867 0.1814 0.1788 0.9 0.1841 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 0.1469 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1446 0.1423 0.1401 0.1379 0.1251 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1230 0.1210 0.1190 0.1170 0.1003 1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.0985 0.0951 0.0934 0.0869 0.0853 1.3 0.0968 0.0918 0.0901 0.0885 0.0838 0.0823 0.0808 0.0749 0.0721 1.4 0.0793 0.0778 0.0764 0.0735 0.0708 0.0694 0.0681 0.0630 0.0571 1.5 0.0668 0.0655 0.0643 0.0618 0.0606 0.0594 0.0582 0.0559 0.0548 0.0526 0.0505 0.0465 0.0455 1.6 0.0537 0.0516 0.0495 0.0485 0.0475 0.0418 1.7 0.0446 0.0436 0.0427 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 0.0359 0.0329 0.0307 0.0294 1.8 0.0351 0.0344 0.0336 0.0322 0.0314 0.0301 0.0239 0.0233 1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.0129 0.0113 2.2 0.0139 0.0136 0.0132 0.0125 0.0122 0.0119 0.0116 0.0110 2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 0.0073 0.0066 0.0064 2.4 0.0082 0.0080 0.0078 0.0075 0.0071 0.0069 0.0068 0.0062 0.0054 0.0049 2.5 0.0060 0.0059 0.0057 0.0055 0.0052 0.0051 0.0048 0.0040 0.0038 0.0037 2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0039 0.0036 0.0033 0.0031 0.0027 0.0026 2.7 0.0035 0.0034 0.0032 0.0030 0.0029 0.0028 0.0026 0.0023 0.0020 0.0019 2.8 0.0025 0.0024 0.0023 0.0022 0.0021 0.0021 0.0014 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 2.9 0.0011 0.0011 3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0010 0.0010

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