The materials below in red are copied directly from a textbook. Please use the following information to answer the questions on additional materials named “TASK”. Refer to the questions on the additional attached document “TASK” to see if you just need to use Problem 1 of text page 102 below, or if you also need to take into account the question 1 and 2 under Problem 1 of text page 102 shown below. Just because the information is here does not necessary mean they are related to or have to be used o answer questions of additional document “TASK”.
Text Page:
Problem 1: here is an IC factory which the probability of defective product produced is at 0.02%.
Question 1: Write the Binomial Distribution and Poisson distribution of probability of defective product at 5% when 200,000 products are produced.
Question 2: When 100,000 products are produced as one lot, an average of how many defective products will be in one lot.
YOUR TASK
Instructions:
Your work is to use Problem 1 of textbook p.102 to answer the following questions (refer to other additional material)
Please make sure you label which histogram belongs to which, as to there will be multiple histograms in one question. Also, please paste the histogram you made to the word document (here) as well as upload the original excel worksheet in which you did your work so I can always go back and edit the title, etc.
Note:
When density function f(x) is provided, and when x of f(x) is added from 0 to t ≤ n (t is less than or equal to n), it is called cumulative distribution function. When using excel to calculate the cumulative distribution function, you use the following:
• Binomial Distribution =BINOM.DIST(x, n, p, TRUE)
• Poisson Distribution =POISSON.DIST(x, , λ, TRUE)
Question 1: Please use excel to draw probability map (histogram) of binomial distribution and poisson distribution when observed value is at 80. Then use excel to draw a overlapped histogram (overlap of binomial distribution and poisson distribution) when observed valued is from 20 to 60. (This means question 1 needs to have 3 histograms in total (binomial distribution when observed value at 80, poisson distribution when observed value is at 80, and overlap of binomial and poisson distribution when observed value is from 20 to 60)
Question 2: Using the information given above regarding standard deviation of binomial distribution and poisson distribution to find the standard deviation, and please examine/compare and discuss it with relations to the graph/histogram you made in Question 1 above.
Question 3: Please make a line graph of binomial and poisson distribution’s cumulative distribution from 0 to adequate (random) number. Please make sure they (binomial and poisson distribution’s cumulative distribution ) will surpass 80 percent, and clearly specify at what point (where) the observed value will be when the cumulative distribution also surpass 80 percent.
Note: Please remember to paste the graph/histogram you made in excel here in order. Make sure you label and name the axis and the title of the graph. When you are putting two graphs (making overlapping graphs), make sure you have different colors for the bar.
Also remember to upload not only the word document in which you posted the graphs/histogram you made on excel but also upload the excel workbook and worksheet in which you did your work on so if I ever need to change the color of the graph or change the title or axis, I can.