I need help with 8 statistics questions

I need 8 statistics questions answered

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Show all work to receive full credit when appropriate. 1. The average monthly mortgage payment is \$982 in the United States. If the standard deviation is \$180 and the mortgage payments are normally distributed, find the probability that a randomly selected monthly payment is a) More than \$1500 b) Less than \$850 c) Between \$800 and \$1150 d) If the probability is 0.6950 that a monthly mortgage payment is less than X amount, find the value of X. 2. The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was \$26,489. If the population standard deviation is \$3204 and 36 institutions are randomly selected, find the probability that the sample mean cost for these 36 schools is a) Less than \$25,000 b) Between \$26,000 and \$27,000 3. A political candidate estimates that 30% of the voters in her party favor her proposed tax reform bill. If there are 400 people at a rally, find the probability that at least 100 voters will favor her tax bill. 4. It is desired to estimate the mean GPA of each undergraduate class at a large university. The population standard deviation is 1.2. How large a sample is needed to estimate the GPA within 0.25 at the 90% confidence level? 5. A random sample of 50 cars in the drive-thru of a fast food restaurant revealed an average bill of \$18.21 per car. The population standard deviation is \$5.92. Estimate the mean bill for all cars from the drive-thru with 95% confidence. 6. A meteorologist who sampled 13 randomly selected thunderstorms found that the average speed at which they traveled was 15.0 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the mean. Assume the variable is normally distributed. 7. The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Estimate the population mean size of a university dance company with 90% confidence. Assume the variable is normally distributed. 21 25 32 22 28 30 29 30 40 32 8. Approximately 10.3% of American high school students drop out of school before graduation. If a random sample of 10 students is selected at random, find the probability that at most 2 students drop out using the binomial formula. Formula:

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