Question: Problem 8, please show work Problem 8: A random sample of 81 executives (these 81 include both male and female) is drawn for the purpose

Problem 8, please show work

Problem 8: A random sample of 81 executives (these 81 include both male and female) is drawn for the purpose of estimat ing the population proportion of females and the mean age of all female executives. The sample contains 33 fe- male executives and for those ladies, the sample mean and standard deviation are 46.5 years and 6.8 years, re- spectively. We first want to build a confidence interval for the proportion of female executives in the population a. Check that the conditions to build a confidence interval are satisfied. State whether the critical value is from a Z-distribution or a T-distribution and why. b. Find the margin of error for a 95% confidence interval. Round to the nearest thousandth. c. Find a 95% confidence interval for proportion of female executives. Round to the nearest thousandth. d. Interpret the confidence interval. e. Based on your confidence interval, is it reasonable to state that half of all executives are female

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