The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30000 and $60000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers as $16642. Assume the standard deviation =$2400. What is the probability that a sample of 100 taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean?