Question

1. Making handerafted pottery generally takes two major steps: wheel throwing and firing The time of wheel-throwing and the time of firing means of 30 minutes and 50 minutes and standard deviations of 2 minutes and I minute, respectively. (1 point) a. What is the probability that a piece of pottery will be finished within 95 minutes? normally distributed random variables with are b. What is the probability that it will take longer than 110 minutes? TABLE 111 Cumulative Standard Normal Distribution (Continued 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0 0.500000 0.08 0.503989 0.09 0.507978 0.547758 0511967 0.515953 0.555760 0.519939 0.532922 0.1 0.527903 0.539828 0.2 0.531881 0.543795 0.535856 0.551717 0.559618 0.563559 0.567495 0.606420 0.571424 0.579260 0.3 0.583166 0.575345 0.614092 0.651732 0.587064 0.590954 0.629300 0.666402 0.594835 0.598706 0.602568 0.640576 0.610261 0.648027 0.684386 0.617911 0.4 0.621719 0.625516 0.633072 0.670031 0.636831 0.673645 0.708840 0.644309 0.680822 0.655422 0.5 0.659097 0.662757 0.677242 0.691462 0.6 0.725747 0.687933 0.694974 0.698468 0.701944 0.705401 0.712260 0.745373 0.715661 0.719043 0.722405 0.729069 0.732371 0.735653 0.738914 0.742154 0.773373 0.748571 0.751748 0.754903 0.7 0.758036 0.761148 0.764238 0.770350 0.767305 0.776373 0.779350 0.807850 0.782305 0.785236 0.8 0.788145 0.815940 0.791030 0.818589 0.793892 0.796731 0.823815 0.799546 0.802338 0.828944 0.805106 0.810570 0.813267 0.9 0.821214 0.826391 0.831472 0.833977 0.857690 0.836457 0.838913 1.0 0.841345 0.843752 0.846136 0.850830 0.848495 0.853141 0.855428 0.876976 0.896165 0.859929 0.862143 0.864334 0.884930 0.903199 1.1 0.866500 0.868643 0.872857 0.874928 0.870762 0.890651 0.878999 0.881000 0.882977 1.2 0.886860 0.888767 0.892512 0.894350 0.897958 0.899727 0.901475 1.3 0.904902 0.908241 0.906582 0.909877 0.911492 0.913085 0.914657 0.917736 0.916207 1.4 0.919243 0.920730 0.922196 0.923641 0.925066 0.926471 0.927855 0.929219 0.930563 0.931888 1.5 0.933193 0.934478 0.946301 0.935744 0.936992 0.938220 0.939429 0.940620 0.941792 0.942947 0.953521 0.944083 1.6 0.945201 0.950529 0.947384 0.949497 0.948449 0.951543 0.952540 0.954486 1.7 0.955435 0.956367 0.957284 0.958185 0.959071 0.959941 0.963273 0.960796 0.961636 0.962462 1.8 0.964070 0.965621 0.966375 0.973197 0.967116 0.964852 0.967843 0.969258 0.970621 0.968557 0.969946 1.9 0.971283 2.0 0.982136 0.972571 0.973810 0.974412 0.976705 0.971933 0.975002 0.980301 0.975581 0.980774 0.976148 0.979325 0.979818 0.984222 0.981691 0.977250 0.977784 0.978308 0.978822 0.981237 0.983823 0.985738 0.984614 0.988089 0.985371 2.1 0.982571 0.982997 0.983414 0.984997 0.987776 0.988396 0.988989 0.986791 0.987126 0.987455 0.988696 2.2 0.986097 0.986447 0.991576 0.990358 0.990613 0.990863 0.991106 0.991344 2.3 0.989276 0.989556 0.989830 0.990097 0.993053 0.993431 0.993613 0.992656 0.992857 0.993244 0.992451 0.991802 0.992240 2,4 0.992024 0.994766 0.994915 0.995060 0.995201 0.994457 0.994614 0.994297 0.994132 2.5 0.993790 0.993 0.996427 0.996093 0.996207 0.996319 0.995855 0.995975 0.995731 0.995604 0.995473 2.6 0.995339 0.997020 0.997110 0.997197 0.997282 0.997365 0.996928 0.996736 0.996833 0.996533 0.996636 2.7 0.998074 0.997882 0.997948 0.998012 0.997814 0.997744 0.997673 0.997599 0.997523 2,8 0.997445 0.998559 0.998605 0.998462 0.998511 0.998411 0.998359 0.998305 0.998250 0.998193 2,9 0.998134 0.998999 0.998856 0.999184 0.998930 0.998965 0.998893 0.998817 0.998777 0.998736 0.998694 0.998650 3.0 0.999289 0.999264 0.999211 0.999238 0.999155 0.999126 0.999096 0.999032 0.999065 3.1 0.999499 0.999443 0.999462 0,999481 0.999402 0.999423 0.999381 0.999359 0.999336 0.999313 3.2 0.999650 0.999624 0.999638 0.999596 0.999610 0.999581 0.999550 0.999566 0.999533 0.999517 3.3 0.999758 0.999709 0.999720 0.999730 0.999815 0.999749 0.999740 0.999698 0.999687 0.999675 0.999663 3.4 0.999835 0.999828 0.999821 0.999800 0.999807 0.999792 0.999784 0.999776 0.999767 3.5 0.999888 0.999883 0.999879 0.999869 0.999874 0.999864 0.999858 0.999853 0.999847 0.999841 3.6 0.999922 0.999925 0.999918 0.999912 0.999915 0.999908 0.999904 0.999900 0.999896 0.999892 3.7 0.999948 0.999950 0.999946 0.999941 0.999943 58 0.9 0.999936 0.999933 0.999931 0,999967 0.999928 3.8 0.999966 0.999964 0.999963 0.999961 0.999959 0.999958 0.999956 0.999954 3.9 0.999952

Answer 1

Adding the means, gives you:

μ=30+ 50 =80

Adding the variances, gives you:

σ²=2²+1²=5

a)

p (z95- 80(z<6.708) 0.999968 5

b)

110 80 p (z > -)= (z > 13.41) 1- 0.999968 0.000032