MATH 225N Week 5 Assignment; Understanding Normal Distribution (March Term)

1. Question: Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(149,14). 2. Question: Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable. 3. Question: Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable. 4. Isabella averages 17 points per basketball game with a standard deviation of 4 points. Suppose Isabella's points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(17,4). 5. Question: Suppose X∼N(13.5,1.5), and x=9. Find and interpret the z-score of the standardized normal random variable 6. Question: Suppose X∼N(10,0.5), and x=11.5. Find and interpret the z-score of the standardized normal random variable. 7. Question: Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie's points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(23,4). 8. Question: Suppose X∼N(9,1.5), and x=13.5. Find and interpret the z-score of the standardized normal random variable. 9. Question: Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). 10. Question: Suppose X∼N(5.5,2), and x=7.5. 11. Question: Jerome averages 16 points a game with a standard deviation of 4 points. Suppose Jerome's points per game are normally distributed. Let X = the number of points per game. Then X∼N(16,4). 12. Question: John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,11). 13. Question: Suppose X∼N(16.5,0.5), and x=16. 14. Question: Gail averages 64 words per minute on a typing test with a standard deviation of 9.5 words per minute. Suppose Gail's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(64,9.5). 15. Question: William averages 58 words per minute on a typing test with a standard deviation of 10.5 words per minute. Suppose William's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,10.5). 16. Question: Hugo averages 22 points per basketball game with a standard deviation of 4 points. Suppose Hugo's points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(22,4). 17. Question: In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches. Suppose X, height in inches of adult women, follows a normal distribution. Let x=68, the height of a woman who is 5' 8" tall. Find and interpret the z-score of the standardized normal random variable. 18. Question: Suppose X∼N(16.5,2), and x=18.5. 19. Question: Suppose X∼N(6.5,1.5), and x=3.5. 20. Question: Suppose X∼N(20,2), and x=26. 21. Question: Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5).