6.1 The Standard Normal Distribution words. X = 1. A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces, Define the random variable X in 2. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median? 3. X ~ N(1, 2) 0 = 4. A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = 5. X ~ N(-4, 1) What is the median? 6. X ~ N(3, 5) 0 = 7. X ~ N(-2, 1) H= 8. What does a z-score measure? 9. What does standardizing a normal distribution do to the mean? 10. Is X ~ N(0, 1) a standardized normal distribution? Why or why not? 11. What is the z-score of x = 12, if it is two standard deviations to the right of the mean? 12. What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean? 13. What is the z-score of x = -2, if it is 2.78 standard deviations to the right of the mean? 14. What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean? 15, Suppose X ~ N(2, 6). What value of x has a z-score of three? 16. Suppose X ~ N(8, 1). What value of x has a z-score of -2.25? 17. Suppose X ~ N(9, 5). What value of x has a z-score of - 0.5? 18. Suppose X ~ N(2, 3). What value of x has a z-score of -0.67? 19. Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean? 20. Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean? 21. Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean? 22. Suppose X ~ N(-1, 2). What is the z-score of x = 2? 23. Suppose X ~ N(12, 6). What is the z-score of x = 2? 24. Suppose X ~ N(9, 3). What is the z-score of x = 9? 25. Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5? 26, In a normal distribution, x = 5 and z - -1.25. This tells you that x = 5 is_ standard deviations to the (right or left) of the mean. 27, In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is standard deviations to the (right or left) of the mean. 28. In a normal distribution, x = -2 and z = 6. This tells you that x = -2 is standard deviations to the (right or left) of the mean, 29. In a normal distribution, x = -5 and z = -3.14. This tells you that x = -5 is_ standard deviations to the (right or left) of the mean