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Applied Statistics

An investment center has been running investment courses for many years. According to records, 28% of students who have attended the investment course can earn a profit of more than 2% within one week by the end of the course. Currently, there are 20 students attending an investment course. The trading technique of each student is independent.



  2. (a)  Most likely, how many students in this course can earn a profit of more than 2% within one week by the end of the course? What is the corresponding probability? (Justify your answer with the calculation of the probabilities of the two outcomes with the highest probabilities.)



  4. (b)  What is the probability that at most 2 students can earn a profit of more than 2% within one week by the end of the course?



  6. (c)  The investment center would give an award to every student by the end of the course. Cash award of $1400 will be given to those students who can earn a profit of more than 2% within 1 week and $100 will be given to those students who fail to earn a profit of more than 2% within 1 week. For many courses with 20 students each, calculate the following information about the total amount of cash award given to students in a course:



    2. (i)  the minimum total amount,



    4. (ii)  the maximum total amount,



    6. (iii)  the most likely total amount,



    8. (iv)  the expected total amount, and



    10. (v)  the standard deviation of total amount. 




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