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Note: This question has two parts "A" and "B", solve them independently. Keep four decimal places. PART -"A" SRP Inc ranked in top twenty organizations in Canada. They have fifty two percent male engineers and forty eight percent female engineers. The starting salaries of female engineers are normally distributed with mean of $69,500 and a standard deviation of $17,000. The starting salaries of male engineers are also normally distributed with a mean of $66,355. A random sample of fifty female engineers and a random sample of sixty male engineers are selected. Furthermore, the variance of the difference between two means of starting salaries of selected female and male engineers is calculated as 9,284,209. (A-1) What is the probability that the mean starting salary of selected female engineers are at least $2,220 higher than the mean starting salary of selected male engineers? (A-2) For a female engineer, what starting salary is closest to the 63"d percentile? PART -"B" The chairman of the statistics department in a certain college believes that seventy percent of the department's graduate assistantships are given to international students. A random sample of fifty graduate assistants is taken. (B-1) Find the standard error of the sampling proportion. (B-2) What is the probability that the sample proportion is within +0.05 of the population proportion