Suppose ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 6. A university plans to award scholarships to students whose scores are in the top 4%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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- Select a significance level α and reject the null-hypothesis if the p-value is less than α. Explain, in complete sentences, your findings: Is there a statistically significant association (at α level) between the provided genes? What is the magnitude and the direction of the association?The report “Parents, Teens and Digital Monitoring” (Pew Research Center, January 7, 2016,pewinternet.org/2016/01/07/parents-teens-and-digital-monitoring, retrieved April 4, 2018)reported that 61% of parents of teens age 13 to 17 said that they had checked which websitestheir teens had visited. The 61% figure was based on a representative sample of 1060 parents ofteens in this age group. Construct and interpret a 90% confidence interval for the proportion ofall parents of teens age 13 to 17 who have checked which web sites their teens visit.13) For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. What is the probability of Z obt? (round to the nearest…
- A Gallup Poll of U.S. adults indicated that Kentucky is the state with the highest percentage of smokers (Gallup.com, December 2015). Consider the following example data from the Tri-State region, an area that comprises northern Kentucky, southeastern Indiana, and southwestern Ohio.9 For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. What kind of test will you need to perform?…9) For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. What kind of test will you need to perform?
- 3) For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. What's the Null and Alternate?14) For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. Do you retain or reject the null hypothesis?10) For this problem you will need: pencil, paper, calculator, z-crit significance levels. and a NC probability calculator, Z-Crits for Common Significance Levels https://docs.google.com/document/d/1bkcDAOsof2cceLd0qhIhiyJ4C09VkQwSuGUcOTQLLpI/edit?usp=sharing Normal Curve Probability Calculator https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. What is the Z crit? 1) 1.96 2) +- 1.645 3) +2.58 4) 2.326
- Give 2 examples of Mode in Measure of central tendency to ungrouped dataRussia has recently started a push for stronger smoking regulations much like those inWestern countries concerning cigarette advertising, smoking in public places, and soon. The DATAfile named Russia contains sample data on smoking habits of Russiansthat are consistent with those reported by the Wall Street Journal (the Wall StreetJournal, October 16, 2012). Analyze the data using Excel and answer the followingquestions.a. Develop a point estimate and a 95% confidence interval for the proportion of Russianswho smoke.b. Develop a point estimate and a 95% confidence interval for the mean annual per capitaconsumption (number of cigarettes) of a Russian.c. For those Russians who do smoke, estimate the number of cigarettes smoked per day.Which scenario will produce a larger test statistic