So I've translated this assignment from another language, but hope it's good enough translated/understandable. 1. The problem statement, all variables and given/known data According to the Statistics of Denmark, there was in the construction sector in the period 2009-2011 an average of 920 business bankruptcies per year out of a total population of 32.100 companies. These figures are considered to be representative of the construction sector (hereinafter abbreviated C-sector) for the period from 2009 and onwards. The number of businesses in the C-sector is specifically assumed to be constant from the year 2009 and onwards a) Explain the conditions under which the number of business bankruptcies in the C-sector during 2014 can be assumed to be binomially distributed. Discuss the extent to which these assumptions are likely to be met in practice. The number of business bankruptcies in the C-sector during 2014, XC, is hereinafter assumed to be binomially distributed with parameters nC and PC. b) Specify an estimate for PC. Specify an estimate for the expected number of bankruptcies in the C-sector during 2014. Calculate the variance of the estimator of PC. Calculate the variance of the estimator of the expected number of bankruptcies in the C-sector during 2014. c) Explain that the number of bankruptcies in the C-sector during 2014 can be assumed to be approximately normally distributed. Specify the parameters of the approximate normal distribution. d) Specify an approximate 95% confidence interval for PC. Specify an approximate 95% confidence interval for the expected number of bankruptcies in the C-sector during 2014. e) Explain the reason, that we in question 1c) can conclude, that the number of business bankruptcies in the C-sector during 2014 is approximative binomially distributed, when we already know that the number actually is (exact) binomially distributed. 2. Relevant equations (I apologize, but I simply cannot find the "sigma symbol in the toolbar" for making complex equations. Reason they are written like this is not a lack of effort, but I've spent a good 5 minutes only looking for that thing! Hope they are understandable though) P(-Zα/2 < (Y - θ)/(√Var(Y)) < Zα/2 ]Y-Zα/2*√Var(y) ; Y+Zα/2*√Var(Y)[ 3. The attempt at a solution I'm not really sure about a). I can say they are binomially distributed because either the business got bankrupt, or they dont. They have 2 outcomes, where success in this case is bankruptcy, and both outcomes are independent of each other, hence they are binomially distributed. Is this right? no clue how to discuss the extent to which these assumptions are likely to be met in practice, hmpf. b) The estimate for Pc is P-hat = X/n = 920/32100 = 0,02866 The estimate for the expected bankruptcies is given in the text itself I believe? Which is X=920. So that's P-hatX = 920 The variance for the estimate PC is Var(PC)=nP(1-P) = 32100*0,02866(1-0,02866) = 29,89 The variance for the estimate of the expected value is? This is where it goes wrong for me .. Surely I cant do the nP(1-P) again .. 32100*920(1-920) .. it will give me a minus number.. So where did I mess up? Thanks in advance. And if part of the assignment text isn't understandable/poorly written, tell me, and I can try and re-translate it.