Question

Please help with 3 and 4!

After graduation you join a company that produces widgets. The manufacturing process is known to produce defective widgets with a probability of 0.15. 1) You take a sample of 20 widgets and find the number of defective widgets. a. What is the theoretical name of this distribution? b. Create 10,000 samples of this distribution in R. Plot the histogram. Print and turn in the histogram with your name. What is the average of the 10000 samples (for this simulation experiment)? What is the theoretical mean? Is the simulation mean consistent with theoretical mean? C. 2) You keep inspecting the widgets till you find a defective widgets. You count the number of widgets inspected. a. What is the theoretical name of this distribution? b. Create 10,000 samples of this distribution in R. Plot the histogram. Print and turn in the histogram with your name. What is the average of the 10000 samples (for this simulation experiment)? What is the theoretical mean? Is the simulation mean consistent with theoretical mean? 3) You keep inspecting the widgets till you find 3 defective widgets. You count the number of widgets inspected. a. What is the theoretical name of this distribution? b. Create 10,000 samples of this distribution in R. Plot the histogram. Print and turn in the histogram with your name. What is the average of the 10000 samples (for this simulation experiment)? What is the theoretical mean? Is the simulation mean consistent with theoretical mean? 4) 30 defective and 70 non-defective widgets are mixed in a box. You take a sample of 10 widgets from this box and determine the number of defective widgets. a. What is the theoretical name of this distribution? b. Create 10,000 samples of this distribution in R. Plot the histogram. Print and turn in the histogram with your name. What is the average of the 10000 samples (for this simulation experiment)? What is the theoretical mean? Is the simulation mean consistent with theoretical mean?

Answer 1

R RGui (64-bit) - [R Console] R File Edit View Misc Packages Windows Help > ##3) > P=0.15 > n=3 > #a) The therotical distribution is Binomial distribution > #The Trials are independent and only two outcome possible. > #b) > x=rbinom (10000, 3,0.15) > length (x) [1] 10000 > hist(x) > #c) > xbar=mean (x) > xbar [1] 0.4403 > T mean=n*P # #Therotical mean > I mean [1] 0.45 > ## Therotical mean and actual meam is approximetly same

R RGui (64-bit) - [Untitled - R Editor] R File Edit Packages Windows Help ##3) P=0.15 n=3 #a) The therotical distribution is Binomial distribution #The Trials are independent and only two outcome possible. #b) x=rbinom (10000,3,0.15) length(x) hist (x) #c) xbar=mean (x) xbar T_mean=n* ##Therotical mean T_mean ## Therotical mean and actual meam is approximetly same

Histogram of x 5000 6000 Frequency 3000 4000 11 1000 2000 0 0.0 0.5 1.0 1.5 20 25 3.0