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11. Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However,since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?A. State the hypothesis you will test. (2 pts)B. Calculate the test statistic. (2 pts)C. Find the P-value. (2 pts)D. What is the conclusion? (2 pts)12. Calculate a Z score when X = 20, μ = 17, and σ = 3.4. (2 pts)13. Using a standard normal probabilities table, interpret the results for the Z score in Problem 12. (2 pts)14. Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability.Based on your findings, should you give her a raise? Explain your reasoning as to why or why not. (2 pts)
15. Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points. a. Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? (2 pts)b. Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring? (2 pts)