The normal distribution

1. In a normal distribution, a data value located 0.9 standard deviations below the mean has Standard Score: z= In a normal distribution, a data value located 2.4 standard deviations above the mean has Standard Score: Z= In a normal distribution, the mean has Standard Score: z = 2. A variable xx is normally distributed with mean 21 and standard deviation 3. Round your answers to the nearest hundredth as needed. a) Determine the z-score for x=29. b) Determine the z-score for x=12. Z= c) What value of xx has a z-score of 3? X= d) What value of xx has a z-score of -1? X= e) What value of xx has a z-score of 0? X= 3. A variable is normally distributed with mean 20 and standard deviation 6. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.| a) Find the area to the left of 22. b) Find the area to the left of 12. c) Find the area to the right of 18. d) Find the area to the right of 24. e) Find the area between 12 and 30. 4. The weights of a certain dog breed are approximately normally distributed with a mean of 49 pounds, and a standard deviation of 5.7 pounds. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) Find the percentage of dogs of this breed that weigh less than 49 pounds. = b) Find the percentage of dogs of this breed that weigh less than 46 pounds. c) Find the percentage of dogs of this breed that weigh more than 46 pounds. = 5. The annual rainfall in a certain region is approximately normally distributed with mean 41.9 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 44 inches? % b) What percentage of years will have an annual rainfall of more than 39 inches? % c) What percentage of years will have an annual rainfall of between 38 inches and 42 inches