The US census revealed the probability distribution of the starting letter used in a surname/last names to be:

1st Letter in Last Name	A	B	C	D	E	F	G	H	I
Percentage %	3.6%	8.8%	7.7%	4.6%	1.9%	3.5%	5.4%	7.3%	0.4%
1st Letter in Last Name	J	K	L	M	N	O	P	Q	R
Percentage %	3%	3.3%	4.8%	1.5%	9.9%	1.9%	4.9%	0.2%	5.8%
1st Letter in Last Name	S	T	U	V	W	X	Y	Z
Percentage %	9.6%	3.5%	0.3%	1.6%	5.9%	0.2%	0.1%	0.3%

University has 35,000 students enrolled, and that the surnames/last names of any indicated populations or sub-populations follow the above given distribution. Part a)__________________________________________________________________ Let's say that 1138 students from the faculty of Science are selected for a certian scholarship in the Fall term. What is the probabability that, at least 13 but at most 21, of those Science student award winners will have a surname starting with M?

Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Gamma B. Binomial C. Uniform D. Negative Binomial E. Normal F. Hypergeometric G. Beta H. Poisson I. None of the above Give the probability that X is at most 21 and at least 13? Part b)__________________________________________________________________ Let's say that this Univeristy can process 2195 applications per day. If a month is considered to be 30 days, and each day has 24 hours, what is the probability that at least 0 but at most 2 hours will go by without processing an application from students with surnames starting with O? Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Beta B. Gamma C. Negative Binomial D. Binomial E. Hypergeometric F. Uniform G. Normal H. Poisson I. None of the above Give the probability that X is at most 2 and at least 0. Part c)__________________________________________________________________ If each student's performance (which was found to be any score from 0% to 100% with equal likelihood) was independent; what is the probability that, if 1717 questions were asked through out the course of a semester, the proportion of the number of questions students with surnames starting with the letter Y got correct, is at least 0.33 but at most 0.52?

Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Hypergeometric B. Gamma C. Beta D. Poisson E. Negative Binomial F. Binomial G. Normal H. Uniform I. None of the above Give the probability that X is at most 0.52 and at least 0.33. Part d)__________________________________________________________________ Let's say that this Univeristy can process 2195 applications per day. If a month is considered to be 30 days, and each day has 24 hours, what is the probability that at least 51 but at most 68 applications from students with surnames starting with Y in a month?

Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Beta B. Gamma C. Uniform D. Binomial E. Negative Binomial F. Poisson G. Normal H. Hypergeometric I. None of the above Give the probability that X is at most 68 and at least 51. Part e)__________________________________________________________________ If students were selected at random, but with replacement, what is the probability that it takes at least 5328 but at most 8750, to select the 20th student with the surname starting with a U?

Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Poisson B. Uniform C. Binomial D. Normal E. Beta F. Gamma G. Hypergeometric H. Negative Binomial I. None of the above Give the probability that X is at most 8750 and at least 5328. Part f)__________________________________________________________________ If every student is just as likely to ask and repeat asking questions; what is the probability that, out of 1717 questions asked, the number of questions asked by people with surnames starting with the letter B is at least 136 but at most 166?

Select a Random Variable X that will help you to solve this problem. Select the correct distribution(s) of X. A. Normal B. Negative Binomial C. Gamma D. Beta E. Binomial F. Uniform G. Poisson H. Hypergeometric I. None of the above Give the probability that X is at most 166 and at least 136?