You may need to use the appropriate appendix table or technology to answer this question.Nominal income refers to an income value that is not adjusted for inflation. Real income adjusts the nominal value for the rate of inflation. Real income per capita is considered a good measure of the buying power of an individual in a particular area because it adjusts for both the number of people in the area and the relative inflation of the area. According to Forbes magazine, the state with the highest annual real income per capita in $2020$ is Connecticut with a real per capita income of $$68,533.$ Suppose that the annual real income of individuals in Connecticut follows a normal distribution with a mean of $$68,533$ and standard deviation of $$23,480.($a$)$What is the probability that an individual in Connecticut has an annual real income of $$51,000$ or more? $($Round your answer to four decimal places.$)($b$)$What is the probability that an individual in Connecticut has an annual real income of $$27,000$ or less? $($Round your answer to four decimal places.$)($c$)$What is the probability that an individual in Connecticut has an annual real income between $$58,000$ and $$78,000?($Round your answer to four decimal places.$)($d$)$What is the annual real income of a person $($in dollars$)$ in the $99$th percentile of annual real income in Connecticut? $($Round your answer to the nearest dollar.$)$$