Are the events “female” and “opposes capital punishment” mutually exclusive? Explain why or why not.

  INTRODUCTORY STATISTICS ECON1005 Assessment 2: Problem Set #1 Question 1A researcher asked 25 customers: “How much would you pay for a television adapter with Internet Access?” Their grouped responses are as follows:     a) Calculate the mean of the dataset    b) Calculate the variance of the dataset  Question 2A researcher is interested in whether or not University students study for 10 hours or more a week. A sample of 100 students is taken. You are given the following set of information: ·         the probability that a randomly selected student from a University is a female is 0.55·         the probability that a student studies for 10 hours or more a week is 0.60·         given that the student selected studies 10 hours or more a week, the probability that this student is male is 0.4     Use this information to fill in the Table below.                                  Question 3 A random sample of 80 lawyers was taken, and they were asked if they are in favour of or against capital punishment. The following table gives the two-way classification of their responses.                                                                      a) If one lawyer is selected at random from this group, find the probability that this lawyer: i) Opposes capital punishment given that the lawyer is a female                                                       ii) Is a female and favours capital punishment iii) Opposes capital punishment or is a male b) Are the events “female” and “opposes capital punishment” mutually exclusive?Explain why or why not.Solution c) Are the events “female” and “opposes capital punishment” independent? Explain why or why not.