For the first problem, use your calculator. For the second problem, use the random digit table.

For this assignment, explicitly state the 5 steps of a simulation and carry out the simulation. For the first problem, use your calculator. For the second problem, use the random digit table.A nuclear reactor facility has two separate safety systems in place to prevent a nuclear meltdown. They prevent meltdown by shutting down the reactor when the temperature reaches the danger level. The first system shuts down the reactor 80% of the time when the danger level is reached. The second system (which is completely separate from the first) shuts down the reactor 90% of the time when the danger level is reached.a.Use your calculator to do 10 repetitions with the first system alone. Theoretically it should successfully shut it down 16 out of 20 times.b.Use your calculator to do 10 repetitions with the second system alone. Theoretically it should successfully shut it down 18 out of 20 times.c.Use your calculator to do 20 repetitions with the first and second systems working together. The reactor will successfully shut down if one or both systems are not working.

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanationEvery Monday a local radio station gives coupons away to 50 people who correctly answer a question about a news fact from the previous day's newspaper. The coupons given away are numbered from 1 to 50, with the first person receiving coupon 1, the second person receiving coupon 2, and so on, until all 50 coupons are given away. On the following Saturday, the radio station randomly draws numbers from 1 to 50 and awards cash prizes to the holders of the coupons with these numbers. Numbers continue to be drawn without replacement until the total amount awarded first equals or exceeds $300. If selected, coupons 1 through 5 each have a cash value of $200, coupons 6 through 20 each have a cash value of $100, and coupons 21 through 50 each have a cash value of $50.a) Explain how you would conduct a simulation using the random number table provided below to estimate the distribution of the number of prize winners each week. b) Perform your simulation 3 consecutive times, (that is, run 3 trials, one after another.) Start at the leftmost digit in the first row of the table and move across. Make your procedure clear so that someone can follow what you did. You must do this by marking directly on or above the table. Report the number of winners in each of your 3 trials.72749 13347 65030 26128 49067 02904 49953 74674 94617 1331781638 36566 42709 33717 59943 12027 46547 61303 46699 7642338449 46438 91579 01907 72146 05764 22400 94490 49833 09258