Question 4In an international school, each staff has to take place in at least 3 community services in a year. Thefollowing table represents the probability distribution function of the number of community services (X) astaff has been taken in a year.3456.7P(X=x)0.2kk0.350.20.03(a) What is the value of k?(b) Find E(X) and o (X).(c) Suppose the number of community services have been taken by staffs are independent. In a departmentwith 11 staffs, what is the probability that exactly 7 staffs have taken place in at least 5 services?Elementary Statistics

Introduction: The random variable X is the number of community services that a randomly selected…

Question 4 In an international school, each staff has to take place in at least 3 community services in a year. The following table represents the probability distribution function of the number of community services (X) a staff has been taken in a year. X 3 4 P(X x) 0.2k k 0.35 0.2 0.03 (a) What is the value of k? (b) Find E(X) and o (X). (c) Suppose the number of community services have been taken by staffs are independent. In a department with 11 staffs, what is the probability that exactly 7 staffs have taken place in at least 5 services?