The number of students taking the Scholastic Aptitude Test (SAT) has risen to an all-time high of

Question:

The number of students taking the Scholastic Aptitude Test (SAT) has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.
Number of Number of
Times Students
1 ............ 721,769
2 ............ 601,325
3 ............ 166,736
4 ............ 22,299
5 ............ 6,730
a. Let x be a random variable indicating the number of times a student takes the SAT.
Show the probability for this random variable.
b. What is the probability that a student takes the SAT more than one time?
c. What is the probability that a student takes the SAT three or more times?
d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?
e. What is the variance and standard deviation for the number of times the SAT is taken?
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