The annual return of a well-known mutual fund has historically had a mean of about 10% and a standard deviation of 21%. suppose the return for the following year follows a normal distribution, with the historical mean and standard deviation. what is the probability that you will lose money in the next year by investing in this fund?

2. taxes paid for a given income level rosa is getting ready to do her taxes. she is single and lives in denver. rosa earned $60,000 in taxable income in 2015. she reviews the following table, which shows the irs tax rates for a single taxpayer in 2015. on annual taxable the tax rate (percent) up to $9,225 10.0 from $9,225 to $37,450 15.0 from $37,450 to $90,750 25.0 from $90,750 to $189,300 28.0 from $189,300 to $411,500 33.0 from $411,500 to $413,200 35.0 over $413,200 39.6 based on the irs table, rosa calculates that her marginal tax rate is when her annual taxable income is $60,000. rosa calculates that she owes in income taxes for 2015. rosa then calculates that her average tax rate is , based on the annual income level and the amount of taxes she owes for 2015. after figuring out what she owes in taxes in 2015, rosa decides to ask an accountant for tax advice. the accountant claims that he has found a legal way to shelter $4,000 of taxable income from the federal government. the maximum amount that rosa is willing to pay to learn this strategy and reduce her taxable income by $4,000 is . (hint: sheltering some income means finding a legal way to avoid being charged income tax on that income. for example, someone who has $50,000 in taxable income and shelters $10,000 pays income tax on only $40,000.)