Students in a class take a quiz with eight questions. the number x of questions answered correctly can be approximated by the following probability distribution. x 0 1 2 3 4 5 6 7 8

P(x) 0.03 0.02 0.05 0.08 0.11 0.22 0.3 0.14 0.05

a) Use the probability distribution to find the mean of the probability distribution

b) Use the probability distribution to find the variance of the probability distribution

c) Use the probability distribution to find the standard deviation of the probability distribution

d) Use the probability distribution to find the expected value of the probability distribution