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11.5 (New Book) Notes AM Date: __________________________________ Goal: Understand how to identify and analyze normal probability distributions. I. Normal Distributions Criteria for Normal Distribution The Empirical Rule Ex. A normal distribution has a mean of 21 and a standard deviation of 4 A. Find the range of values that represent the middle 68% of the distribution. B. What percent of the data will be greater than 29? Ex. A normal distribution has a mean of 8.2 and a standard deviation of 1.3 A. Find the range of values that represent the middle 95% of the distribution. B. What percent of the data will be less than 4.3%? Ex. The heights of 1800 adults are normally distributed with a mean of 70 inches and a standard deviation of 2 inches. A. About how many adults are between 66 and 74 inches? B. What is the probability that a random adult is more than 72 inches tall? Ex. The number of friends per member in a sample of 820 members is normally distributed with a mean of 38 and a standard deviation of 12. A. About how many members have between 26 and 50 friends? B. What is the probability that a random member will have more than 14 friends? Z-test Ex. Find z if X 18, X 22,s 3.1 Ex. Find X if z 0.73, X 39,s 8.2 Standard Normal Distribution Ex. The number of videos uploaded daily to a video-sharing site is normally distributed with X 181,099 videos and s 35,644 videos. Find each probability and use a graphing calculator to sketch corresponding area under the curve. A. P(180,000 x 200,000) B. P(X 250,000) Ex. The life spans of a certain tread of tire are normally distributed with X 31,066 videos and s 1644 videos. Find each probability and use a graphing calculator to sketch corresponding area under the curve. A. P(30,000 x 32,000) B. P(X 35,000) 11.5 HW: 1-17odd