5. For this question please do not round off the numerical values of your intermediate steps when you do your calculations. Round off your answers only at the end. Childbed fever is a fatal illness that occurs among new born babies and their mothers. William was investigating the prevalence of childbed fever among mothers (together with their new born babies) who were admitted to The General Hospital of City H. These cases of delivery of new born babies had been classied according to three dierent criteria: 0 whether they had been admitted to the First Division or the Second Division of the hospital 0 whether they had contracted childbed fever 0 whether the babies were delivered in the hospital wards or on the way to the hospital (the soecalled \"street births\") Table 1 below summarises the number of delivery cases in each of these categories. Table 1: Number of Delivery of New IBom Babies under Studies Contraction of First Divsion Second Division Childbed Street Fever ' Street Birth Birth Street0 Birth Yes I 274 I420 No I 312 2046 I&-I Total 345 2320 2020 5000 a) (1.5 marks) William was curious how prevalent childbed fever was among cases admitted to the First Division of the hospital. To answer this question, he would like to know, among all the cases admitted to the First Division. what percentage of them had contracted childbed fever. Construct a 95% condence interval for phmg, the proportion of cases admitted to the First Division who had contracted childbed fever. (In doing so, please use your estimate of Pft'rat to work out the standard deviation for pfirst.) Give your answer correct to 4 decimal places. (b) (1.5 marks) William also wondered if childbed fever was more prevalent among mothers who gave babies on the way to the hospital. This meant that he would like to know, among those cases of \"street birth\