The normal distribution

1. A variable is normally distributed with mean 22 and standard deviation 7. 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 23. b) Find the area to the left of 17. c) Find the area to the right of 21. d) Find the area to the right of 29. e) Find the area between 17 and 30. 2. The weights of a certain dog breed are approximately normally distributed with a mean of 52 pounds, and a standard deviation of 5.8 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 52 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. 3. IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = c) In a sample of 700 people, how many people would have an IQ less than 110? d) In a sample of 700 people, how many people would have an IQ greater than 140? = 4. The weight for newborn babies is approximately normally distributed with a mean of 6.7 pounds and a standard deviation of 1.5 pounds. Consider a group of 1300 newborn babies: a. How many would you expect to weigh between 3 and 9 pounds? b. How many would you expect to weigh less than 8 pounds? c. How many would you expect to weigh more than 5 pounds? d. How many would you expect to weigh between 6.7 and 10 pounds? 5. The weights of a certain dog breed are approximately normally distributed with a mean of u = 45 pounds, and a standard deviation of o = 6 pounds. a.) A dog of this breed weighs 56 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. z= b.) A dog has a z-score of -0.58. What is the dog's weight? Round your answer to the nearest tenth as needed. C.) A dog has a z-score of 0.58. What is the dog's weight? Round your answer to the nearest tenth as needed.|