b) Let the number of days when a certain train service is broken in 3 years (1 year is 365 days) be 1 time. (Hint: you may use Poisson's distribution to approximate the Binomial distribution) The Poisson's probability distribution is given by: P(x) - He - with u being x! the average of the variable x. i. What is the probability that the same train service is broken less than 3 times in 5,000 days? ii. What is the probability that the same train service is broken more than 10 times in 10,000 days? (8 marks) C) A certain chip manufacturer produces memory chips with a mean current consumption of 100mA and standard deviation of the current consumption is 5mA. Assume that the chip current consumption follows a normal distribution. We also assume that the resolution of the current measurement is 1mA (smallest difference between chips is 1mA). A standardized normal distribution table is provided at the Appendix of this paper. i. What percentage of the chips will have current consumption that is equal to or larger than 106mA? ii. What percentage of the chips will have current consumption that is between 95mA and 105mA? (8 marks)Question 6. a) A box has 100 balls consisting of 30 red colour balls and 70 green colour balls. On top of that, there are two types of weight for the balls, 1 kg and 2 kg, as shown in the table below. A ball is now picked randomly from the box. Red Green Total 1 kg 20 20 40 2 kg 10 50 60 Total 30 70 100 Calculate: i. Probability of picking a green ball ii. Probability of picking a red ball that is 2 kg. (4 marks)STANDARD NORMAL CURVE AREAS This table gives areas under the standard nominal distribution (, between 0 and r2 0 in steps of 0.01. 2 3 4 7 0120 0160 019 0279 0359 0.1 0470 0517 0557 0596 0636 .0675 0714 0754 0.2 0703 0832 0871 OP10 0948 0987 1026 .1064 1103 1141 0.3 1179 1217 1255 1293 1031 1360 .1406 .144 .1480 1517 0.4 1354 1501 162# 1684 1700 1736 .1771 .1808 1844 1879 0.5 1915 1950 .1905 2019 2054 2088 2123 2157 2190 2224 0.6 2258 2191 2324 2357 2389 2422 2454 2518 2549 0.7 2580 2612 2642 2673 2704 2734 2764 2794 2823 2852 0.S 2081 .2910 2939 2967 2996 3021 3051 3078 3106 3133 0.9 3150 318 3212 3238 3264 3280 3315 3340 3365 3389 1.0 3413 3430 3461 3485 3508 3531 3554 3577 3599 3621 1.1 3643 3653 3708 3729 3740 3770 3790 3810 3830 1.2 3849 3907 392 3944 3962 3920 3997 4015 1.3 4032 40-49 4064 4082 4099 4115 4131 4147 4162 4177 14 4102 4207 4212 4136 4351 4265 4279 4292 4306 4319 1.5 4302 .43-45 4357 4370 4382 394 4406 4410 4-429 .4441 1.6 4452 4453 4474 4484 4405 4505 4515 4525 4535 4545 1.7 4554 .4564 1573 4582 4591 4599 4616 4625 1643 1.8 4541 46-49 4656 4564 4571 4578 4646 4693 1590 4705 1.9 4713 ,4710 4726 4732 4738 4744 4750 4756 4761 4767 2.0 4772 .4778 4783 4780 1793 4798 4803 4808 4812 4817 2.1 4821 4826 4830 4834 4838 4842 4846 4830 4854 4857 4861 .4454 1871 4875 4878 .4801 4834 4587 1890 2.3 4893 4895 4890 4901 4904 4906 4909 4911 4913 1916 2.4 4918 4920 4021 4035 1027 4020 4031 4932 4034 4036 2.5 4938 49-40 4941 4943 4945 4946 4943 .4949 4951 4952 2.6 4953 4935 4058 4057 4059 4060 4081 4062 4963 4064 4965 4956 1967 4960 4969 4970 .4971 4972 .4973 1974 2.8 4974 4975 4976 4977 4977 4978 4079 4079 4980 4981 2.9 4983 4942 4983 .4984 4984 .4985 .4985 4986 4986 3.0 4987 4987 1937 4980 4980 4989 .4949 4909 4990 4990 4900 49 91 4091 4pp1 4002 4082 4092 4092 4093 4993 4993 4994 1994 1994 4994 4994 4995 4995 1995 4905 495 4095 4006 4096 4096 4996 4097 3.4 4997 .49-97 1997 1997 1997 1997 4997 4997 4997 4998 3.5 4998 4998 4998 4093 4908 4098 409 4998 4098 49-DE 4999 1909 4099 4099 4909 4999 4999 4999 4999 4999 4999 4999 4999 4999 4999 1999 4090 4090 4090 4009 4009 4900 4009 4090 4090 4090 5000 50 00 5000 5000 5000 5000 5000 5000 5000 5000STANDARD NORMAL CURVE AREAS This table gives areas under the standard nominal distribution (, between 0 and r2 0 in steps of 0.01. 2 3 4 7 0120 0160 019 0279 0359 0.1 0470 0517 0557 0596 0636 .0675 0714 0754 0.2 0703 0832 0871 OP10 0948 0987 1026 .1064 1103 1141 0.3 1179 1217 1255 1293 1031 1360 .1406 .144 .1480 1517 0.4 1354 1501 162# 1684 1700 1736 .1771 .1808 1844 1879 0.5 1915 1950 .1905 2019 2054 2088 2123 2157 2190 2224 0.6 2258 2191 2324 2357 2389 2422 2454 2518 2549 0.7 2580 2612 2642 2673 2704 2734 2764 2794 2823 2852 0.S 2081 .2910 2939 2967 2996 3021 3051 3078 3106 3133 0.9 3150 318 3212 3238 3264 3280 3315 3340 3365 3389 1.0 3413 3430 3461 3485 3508 3531 3554 3577 3599 3621 1.1 3643 3653 3708 3729 3740 3770 3790 3810 3830 1.2 3849 3907 392 3944 3962 3920 3997 4015 1.3 4032 40-49 4064 4082 4099 4115 4131 4147 4162 4177 14 4102 4207 4212 4136 4351 4265 4279 4292 4306 4319 1.5 4302 .43-45 4357 4370 4382 394 4406 4410 4-429 .4441 1.6 4452 4453 4474 4484 4405 4505 4515 4525 4535 4545 1.7 4554 .4564 1573 4582 4591 4599 4616 4625 1643 1.8 4541 46-49 4656 4564 4571 4578 4646 4693 1590 4705 1.9 4713 ,4710 4726 4732 4738 4744 4750 4756 4761 4767 2.0 4772 .4778 4783 4780 1793 4798 4803 4808 4812 4817 2.1 4821 4826 4830 4834 4838 4842 4846 4830 4854 4857 4861 .4454 1871 4875 4878 .4801 4834 4587 1890 2.3 4893 4895 4890 4901 4904 4906 4909 4911 4913 1916 2.4 4918 4920 4021 4035 1027 4020 4031 4932 4034 4036 2.5 4938 49-40 4941 4943 4945 4946 4943 .4949 4951 4952 2.6 4953 4935 4058 4057 4059 4060 4081 4062 4963 4064 4965 4956 1967 4960 4969 4970 .4971 4972 .4973 1974 2.8 4974 4975 4976 4977 4977 4978 4079 4079 4980 4981 2.9 4983 4942 4983 .4984 4984 .4985 .4985 4986 4986 3.0 4987 4987 1937 4980 4980 4989 .4949 4909 4990 4990 4900 49 91 4091 4pp1 4002 4082 4092 4092 4093 4993 4993 4994 1994 1994 4994 4994 4995 4995 1995 4905 495 4095 4006 4096 4096 4996 4097 3.4 4997 .49-97 1997 1997 1997 1997 4997 4997 4997 4998 3.5 4998 4998 4998 4093 4908 4098 409 4998 4098 49-DE 4999 1909 4099 4099 4909 4999 4999 4999 4999 4999 4999 4999 4999 4999 4999 1999 4090 4090 4090 4009 4009 4900 4009 4090 4090 4090 5000 50 00 5000 5000 5000 5000 5000 5000 5000 5000