Question

8. The proportion of impurities per batch in a chemical product is a random variable that is well modeled by a Beta distribution with a-3 and ß-2. A batch with more than 40% impurities cannot be sold. a. Find the probability that a randomly selected batch cannot be sold because of excessive impurities b. What is the mean proportion of impurities? the variance? (Hint: use an appropriate method) 9. Suppose Y the amount spent on electricity (in dollars) per month for residents has a mean of $83 and a standard deviation of S11. A random sample of 20 resident's electricity bills is found. Approximate the probability the sample mean electricity bill is less than $80.

Answer 1

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otP 34 2 5 25 Sta M dand Deviation (SD)-11 SD

.01 .02 03 .04 .05 06 .07 .09 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 .0008 .0007 .0007 .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 .0031 .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 .0080 .0078 0075 .0073 .0071 0069 .0068 .0066 .0064 2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 0113 .0110 2.1 .0179 .0174 .0170 .0166 .0162.0158 .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 1.7 .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 .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 .12921271 .1251 .1230 .1210 .1190 -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 26762643 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 4443 4602 562 4522 4404 4364 4286 4247