Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 0 1 0.212 | 0.189 2 3 4 5 6 7 8 0.319 | 0.156 | 0.078 | 0.031 | 0.012 | 0.002 | 0.001 | z P(X = =z) a. What is the probability that a randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. What is the probability that a randomly selected student changed his or her major two or more times? d. What is the mean number of times students changed majors? e. What is the standard deviation of X? f. Challenge Question: If a student changes their major at least once, what is the probability they change it more than once?|