A probability mass function for the class sizes at a small college is given in the table below (assume that these are the only allowed class sizes):
Class sizeProbability
10 ............ 0.05
20 ............ 0.15
30 ............ 0.45
40 ............ 0.10
50 ............ 0.10
60 ............ 0.10
70 ............ 0.05
a. What is the expected value of the class size for a class chosen at random?
b. What is the standard deviation of the class size for a class chosen at random?
c. What percentage of classes are within one standard deviation of the mean class size?
d. What is the cumulative distribution function for class size?
e. What is the probability that a class has between 30 and 60 students?
f. Given that a class has at least 30 students, what is the probability that it has strictly less than 60 students?
g. Given that a class has at least 30 students, what is the probability that it has at least 60 students?
h. Given that a class has at least 30 students, what is the probability that it has strictly more than 60 students?
i. Given that a class has at least 30 students, what is the probability that it has at most 60 students?