PrtSer Insert 5. Scores on the verbal ability portion of the GRE follow a normal distribution with a mean of 500 and standard deviation of 115. a. Between what two values do the middle 95% of scores fall? b. If your score is 650, you did better than what percentage of exam takers? c. What is the probability of a score being between 400 and 550? 6. Suppose that 15% of all students at your school ride a bicycle to class each day. Suppose further that you take a random sample of 80 students at your school. a. Is 15% number a parameter or a statistic? Explain briefly. b. Are you guaranteed that 15% of your sample ride a bicycle to class each day? Explain briefly. c. Does the central limit theorem of s sampling distribution of sample proportions apply? Refer to the technical conditions in the central limit theorem. d. Describe the sampling distribution of the sample proportion of these 80 students who ride a bicycle to class each day. Determine the shape, center, and standard deviation of this distribution. Also include a well-labeled sketch of this distribution.7. Students in an introductory statistics class were asked how many states they have visited. The following output pertains to the sample results: 4 12 16 20 24 28 32 States Visited Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum states 50 13.36 1,03 7.27 2.00 7.00 12.00 20.00 31.00 a. Determine a 90% confidence interval for the population mean number of states visited among all students at this university. b. Check and comment on whether the technical conditions of this confidence interval are satisfied. c. For what proportion of students in the sample is the number of states visited within the interval calculated in part a?O Shift C LL O N Q I X 8. It has been conjectured that two-thirds of all students have an active, as opposed to reflective, learning style. Data are available from a large sample of introductory statistics students at a public university in the eastern United States, who took a survey that assessed their learning style as active or reflective. Of the 962 students who participated, 596 were diagnosed as active learners and 366 as reflective learners. Use these sample data to conduct a significance test of the conjecture that two-thirds of all students have an active learning style. Report the hypotheses, test statistic, and p-value. Include a check of technical conditions. Also indicate your test decision at the a = .05 significance level and summarize your conclusion in context. n between the country's9. The scatterplot of 51 countries below shows the relationship between the country's life expectancy and infant mortality rates ( number of deaths per 1000 live births). Collection 1 Scatter Plot 80 70- O O Ctrl Life Exp 60- Home 50- O 40- O 0 40 80 120 InfantMortalityper_1000 a. How would you describe the association? b. Would you describe the direction of the association as positive or negative? c. Which of the following values is the value of the correlation coefficient? 0.8 0.1 0 -0.1 -0.8