I need help with these 5 questions please

Suppose two friends, Michael and Austin, are arguing about Michael's supposed trivia prowess. Michael, a trivia fanatic, wishes to prove his vast trivia knowledge by answering a series of trivia questions. To test this, Austin purchases a book of trivia questions and randomly selects 100 to ask Michael. Assume that for each question, the probability that Michael gives the correct answer is 0.85. What is the probability that Michael will answer at least 80 questions correctly? Use the normal approximation to obtain the result. Give your answer as a decimal precise to at least three decimal places. According to the College Board, SAT critical reading scores from the 2015 school year for high school students in the United States were normally distributed with a mean of 495 and a standard deviation of 116. Use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the SAT in 2015 will have a critical reading SAT score between 400 and 600 points. Give your answer as a percentage rounded to one decimal place. MC] Mike is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he nds that it is 2.23 oz. The manufacturer's website states that the average weight of each stick is 1.85 oz with a standard deviation of 0.18 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.23 oz or greater? Give your answer as a percentage precise to at least two decimal places. You might nd this table of standard normal critical values useful. :M The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 50 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ,u = 28.29 and a = 33.493, respectively. Let X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is E. Use the central limit theorem (CLT) to determine the probability P that the mean taxable wages in James' sample of 50 counties will be less than $26 million. Report your answer to four decimal places. we: Use the CLT again to determine the probability that the mean taxable wages in J ames' sample of 50 counties will be greater than $24 million. Report your answer to four decimal places. W :1 According to data from the 2010 United States Census, 43.1% of Americans over the age of 65 were male. Suppose Maria, a researcher, takes a random sample of 60 Americans over the age of 65 and nds that 18 are male. Let 13 represent the sample proportion of Americans over the age of 65 that were male. What are the mean and standard deviation of the sampling distribution of 13? Provide your answer rounded to three decimal places