Use the following scenario to answer #6 - 11. Show calculator keystrokes as well as answer. A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults over 50, calculate the following probabilities. Round to 4 decimal places. 6. P(exactly 6 wear sunglasses for driving) 7. P(no more than 6 wear sunglasses for driving) 8. P(no fewer than 6 wear sunglasses for driving) 9. P(4, 5, or 6 wear sunglasses for driving) 10. P(at least 7 wear sunglasses for driving) 11. Calculate the mean and standard deviation. Interpret the mean. 12. Find the area under the standard normal curve to the left of z = 1.5. 13. Find the area under the standard normal curve to the right of z = -1.25. 14. Find the area under the standard normal curve between z = -1.5 and z = 2.5. 15. Find the z-score so the area under the standard normal curve to its left is 0.7512. 16. Find the z-score so the area under the standard normal curve to its right is 0.3218. 17. Find the z-scores that separate the middle 40% of the data from the data in the tails For #18-24 use the following scenario. Men's heights are normally distributed with = 68.3 inches and = 1.8 inches. 18. What is the probability that a randomly selected man is shorter than 68 inches? 19. Approximately 40% of men are below what height? (Round to the nearest tenth of an inch) 20. The big and tall men's shop caters to men over 70 inches tall. Approximately what percent of men would find clothes that fit at the store? 21. The middle 60% of men are between ______________ and ______________ inches tall (approximately). 22. What is the probability that a randomly selected man is taller than 69 inches? 23. If 25 men are randomly selected, what is the probability that the mean of their height is shorter than 68 inches? 24. If 36 men are randomly selected, what is the probability that the mean of their height is taller than 69 inches? 25. The reaction time X in minutes of a certain chemical process follows a uniform probability distribution with 5 10. a. Find the probability the reaction time is between 6 and 8 minutes. b. Find the probability the reaction time is between 5 and 8 minutes. c. What is the probability that the reaction time is less than 6 minutes? 26. You play a game where you pay $5 to play. If you win the game, you win $30. The probability of winning the game is 0.1667. Find your expected winnings. Use the Central Limit Theorem and following scenario for #27 and #28. The upper leg length of a 20 to 29 year old man is approximately normal with a mean length of 43.7 cm and standard deviation of 4.2 cm. 27. A random sample of 15 men are selected. Find the mean and standard deviation. 28. A random sample of 15 men are selected. Would it be unusual for the mean upper leg length to be at least 46 cm