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NAME 11-5 DATE PERIOD Practice The Normal Distribution A normal distribution has a mean of 186.4 and a standard deviation of 48.9. 1. What range of values represents the middle 99.7% of the data? 2. What percent of data will be more than 235.3? 3. What range of values represents the upper 2.5% of the data? Find the missing variable. Indicate the position of X in the distribution. 4. σ if μ = 19, X = 21, and z = 1.3 5. μ if σ = 9.8, X = 55.4, and z = −1.32 6. X if z = −2.19, μ = 68.2, and σ = 11.6 7. z if μ = 112.4, X = 119.2, and σ = 11.9 8. TESTING The scores on a test administered to prospective employees are normally distributed with a mean of 100 and a standard deviation of 12.3. a. About what percent of the scores are between 70 and 80? b. About what percent of the scores are between 85 and 115? c. About what percent of the scores are over 115? d. About what percent of the scores are lower than 90 or higher than 100? e. If 80 people take the test, how many would you expect to score higher than 130? 9. TEMPERATURE The daily July surface temperature of a lake at a resort has a mean of 82˚ and a standard deviation of 4.2˚. If you prefer to swim when the temperature is at least 80˚, about what percent of the days does the temperature meet your preference? Chapter 11 33 Glencoe Algebra 2 Lesson 11-5 f. If 75 people take the test, how many would you expect to score lower than 75?