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Please note that this question consists of five parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A college english professor wants to see how reliably the students can distinguish between the “human-written text” and “Gen AI-produced text”. According to some recent research about 70% of the times a randomly chosen student can correctly identify the source.  The instructor shows 15 short passages to his students. Some of these were written by humans whereas the others were GenAI produced (unknown to the students). For each passage, the students were tasked with identifying if it was human or AI written. For a randomly chosen student in the class, let X be the number of incorrect guesses. Assuming guesses are independent: What is the distribution of X? Clearly state the parameters of the distribution.  Write down the probability mass function, for the random variable X defined above. What is the chance that the student correctly identifies the source for all 15 passages (i.e.: zero incorrect guesses)?  What is the chance that the student will make at least one incorrect guess?  What is the probability of making at least one but no more than 6 incorrect guesses.   

Here is a copy of the Z table (Do not click on the downarrow. Click on the file name to open the table within spacer) Z table.pdf  

Suppose we are given the relationship between X and Y where a=`a` and b=`b` We also know that the sample mean for X is  and the sample standard deviation for X is . Find the standard deviation for Y.  

You are allowed one sheet of blank scrap paper for every quiz and exam.

Calculate the mean of  34.6, 82.1, 16.3, 55.6 In the box below type the two separate lines. mydata=c(34.6, 82.1, 16.3, 55.6)mean(mydata) Run it and THEN enter the answer in the window below. Running it does not automatically submit it.  If you cannot see it, use any other R snippet window in this exam that works, or open https://rdrr.io/snippets/ 

Which web browser must be used for all quizzes and exams to ensure Honorlock can record your assessment?

Which historical figure is often associated with the Classical School’s emphasis on “proportional punishment” as a deterrent?

Which below directs us to make decisions based on the greatest “good” for the greatest number?

________ justice is perceived when people view the fairness of a particular outcome.

The length of time between an act and its consequences is known as _______