Submit a PDF of your homework write-up in the HW5 dropbox with all of your script files before the posted due date. The script files must be commented and run without errors. Each problem must have its own m file(s). All plots are to include complete axis labels.
Your write-up will be in a narrative form and written in a word processor (e.g. MS Word). Do not use the "publish" feature in Matlab to make your report. Explain (briefly) how you solved each problem, present the results (including all plots) and then the interpretation of the results. A plot is not the entire answer to a problem. You may include snippets of code in the write up as a reference, but do not paste the entirety of the m file in the report. The report should be self-contained and not require the reader to look at the m file to understand what you did. If a question asks you to show mathematical steps, you may use the equation editor or (neatly) scan in handwritten work and include it in the report.
1. The data contained in blood.csv contains the lifespans (in days) of human red blood cells from a clinical experiment
A. Show a relative-frequency histogram of the lifespan with the number of bins determined by Rice's formula
B. Make an assessment and justify if it is fair to treat the lifespans as a coming from normal distribution
C. Determine the median, 95th and 5th percentiles of the lifespan
2. Simulate the repeated throwing of two random six-sided dice.
A. Show a relative-frequency histogram of the sum of the dice with the number of bins set at eleven (one for each possible combination)
B. Make an assessment if it is fair to treat the sum as a normal distribution
C. Using the results of your simulation, what is the probability of rolling an 11
or 12?
3. The data contained in lobster.csv contains weights of lobsters (in ounces) caught in Massachusetts last year.
A. Show a relative-frequency histogram of the lobster weight with the number of bins determined by Sturges' formula
B. Determine the mean and standard deviation of the weights
C. Make an assessment and justify if it is fair to treat the lobster weights as normally distributed?
D. Lobstermen are able to sell lobsters that weigh over 24oz at an increased price. What percent of the shellfish they catch could they expect to fall into this category? Estimate using
i. The raw data
ii. NORMCDF assuming that the lobster weights are normally distributed
4. A shipping pallet holds ten boxes. Each box contains 255 pieces of part X and 160 pieces of part Y. The weight of part X is normally distributed with a mean of
lb and standard deviation of 0.15 lb. The weight of part Y is uniformly distributed between 1.1 lbs to 1.25 lbs. Using a Monte Carlo simulation:
A. Compute the mean and standard deviation of the weight loaded onto the
pallet.
B. Show a relative-frequency histogram of the weight on the pallet with the number of bins determined by Sturges' formula.
C. Verify that the number of simulations you are running is sufficient by graphically showing convergence in the mean of the weight on the pallet. Display in a plot with the horizontal in log-scale and the vertical in linear-scale. If you find it was not, redo parts (A) and (B).
D. Is it reasonable to treat the weight on the pallet as normally distributed? Explain.
E. A wooden pallet can safely hold a weight of up to 4950 lb. What percentage of the pallets can we expect to be overloaded based on
i. The simulation data
ii. A normal distribution using NORMCDF
5.A machine is being built out of two types of parts: A and B. Part A will work 98% of the time when turned on and part B works 90% of the time when turned on. The machine has 10 of part A and five of part B. For the machine to operate correctly when turned on, all 10 of part A must function and at least 3 of part B must function.
A. What is the probability that the machine will operate correctly when turned on
B. Verify that the number of simulations you are running is sufficient by graphically showing convergence in the probability of successful operation. Display in a plot with the horizontal in log-scale and the vertical in linear-scale. If you find it was not, redo part (A)
Hint: to simulate turning the machine on, you will want to have random numbers that determine the success or failure of each part. Then you will want to test if enough parts work for the machine to function. Repeat this simulation until convergence.