Question

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 2 3 4 5 6 7 8 P(X = a) 0.28 0.238 0.196 0.153 0.073 0.039 0.017 0.003 0.001 a. What is the probability that a randomly selected student changed his or her major at least once? Preview b. What is the probability that a randomly selected student changed his or her major at most twice? Preview c. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times? Preview (Round your answer to three decimal places.)

Answer 1

Xa 0.153 0.073 10.039 0.017 0.003 0.001 0.196 0.98 10.2381 prx?]) = 1- P(x20) Prx? 1) = 1- P(x0) Pard P(x21) = 1 0.28 PCX71) = 0.72 Probability that a randomly selected student changed his or her major least once [0.72 at 0.72 P ( x 2) - P(x=0) + P(X=1) +PCX=2) p(x+2) = 0.18 +0.238 +0.196 P(x+2) = 0.714 The probability that a student changed his or i r 10.714) randomly selected her major at most twice

- (C) my pl change the major.) = P(021) PC change the major) = 1- P(x=0) p (change the major) = 1-0.28 P(change the major) = 0.72 P ( change the major n more than three times) pr change the major n X73) = P(x24) + P(x=5)+ P(736) + P(x =7) + P(X=8) P ( charge the major nx73)= 0.133 P( change the major nx73 / B change the majes) = 0.133 0. 7 = 0.1847 = 10:185