BusinessWeek surveyed students who finished their 30 studies in a master's program (BusinessWeek, September 22 2003). According to this survey, the average annual salary of a woman and a man 10 years after completing their studies is $ 117.000 and $ 168.000, respectively. Consider these amounts as means populations of wages of a woman and a man. Suppose the population standard deviation between the wages of women is $ 25,000 and between the wages of men is $ 40,000. With this information: a) What is the probability that a simple random sample of 40 men the sample mean does not differ more than $ 10,000 average Population of $ 168.000? b) What is the probability that a simple random sample of 40 the sample mean women do not differ more than $ 10,000 average Population of $ 117.000? c) Which of the two cases a) and b) are more likely to get a sample mean not differ by more than $ 10,000 from the population mean? Why? d) What is the probability that a simple random sample of 100 men, the sample mean does not differ by more than $ 4,000 average Population? Note: since the size of populations is not known assume they are endless.