_Question 4: Using the information from the previous question, nd the expected number of people cured, i.e., E(X)(answer in decimal form round to nearest tenth if necessary). mo = Question 5: Now nd the standard deviation of the number of people cured X (answer in decimal form round to nearest tenth if necessary). SD(X) = 2.6833 people Question 6: If 24 of the 30 people were cured, would this be unusual? 0 Yes O No Use J MP to generate 100 replications of draws from a binomial with n = 30 and p = 0.6 (create a new data sheet, ll in the rst column with 100 rows of dots, then use the formula menu to put in a random binomial with n = 30 and p = 0.6). What are the observed mean and standard deviation of your 100 random replications? (Use Basic \"Distributions\" to get these values form JMP and KEEP the variable type CONTINUOUS.) They should be fairly close to your theoretical expected value calculated earlier. Remember this is random, so you should not expect to get the same value as another student. (You will submit the generated data set at the end of this assignment.) Here is an example of what J MP will look like if n = 30 and p = 0.6. Question 7: What is the sample mean, LE : [: Question 8: What is the sample standard deviation, .3 : [: Now, please change the variable type to ordinal (since there is no discrete option), then bring up the distribution once again Via Basic -> Distribution. _Question 9: How many of your 100 replications were 24 or _Question 10: Is this consistent with your answer earlier about whether 24 or more would be unusual? Part III. Binomial Random Variables Recall that the characteristics of a binomial random variable are: 1. The experiment consists of a xed number (we usually use 11) of trials. 2. The trials are independent. 3. There are only two possible outcomes on each trial, which for convenience we call \"success\" and \"failure.\" 4. The probability of a success (p), is the same for each observation. 5. If X is a binomial random variable then its mean is E[X] = pa, = up and its standard deviation is 0m = np(1 p)- For the next three questions of the following examples, decide whether X is a binomial random variable using ONLY the information given. State why or why not. Question 1: The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city, and asked whether he or she opposes the death penalty; X is the number who say \"Yes\". 0 No, more than two outcomes. 0 No, trials are not independent. 0 No, probability is not the same for each person. 0 Yes, meets all requirements of a binomial random variable. Question 2: Suppose a jury of 12 people is chosen from the above pool, and this jury hears a case and discusses the verdict; X is the number who think the defendant is guilty. 0 No, the trials are not independent. 0 No, there are more than two possible outcomes. 0 No, there is not a xed number of trials. 0 Yes, meets all requirements of a binomial random variable. Question 3: A drug is known to be 60% effective in curing a certain disease; that is, the probability is 0.6 that a person with the disease given the drug will be cured. Suppose 30 people with the disease are chosen at random and given the drug. Let X be the number of people among the 30 who are cured. 0 Yes, meets all requirements of a binomial random variable. 0 No, there are more than two possible outcomes. 0 No, the probability of success is not constant. 0 No, trials are not independent