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## Normal Distribution Calculations

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**Using the 4-step Process**• State: Express in terms of the observed variable x. • Plan: Draw a picture of the distribution and shade the area of interest. • Do: Perform calculations • Standardize x • Use the table • Conclude: Write your conclusion in the context of the problem.**When Tiger Woods hits his driver, the distance the ball**travels follows a Normal Distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards? • State: • Plan: • Do: • Conclude: Let x = the distance Tiger’s ball travels and it has a distribution N(304, 8). We want P(x 290). About 96% of Tigers drives travel at least 290 yards.**Scores for a test have a mean of 100 and standard deviation**of 15. Find the probability that a score is below 112.**Every month, American households generate an average of 28**pounds of newspaper for garbage or recycling. Assume =2 pounds. If a household is selected at random, find the probability that it generates between 27 and 31 pounds per month.**An exclusive college desires to accept only the top 10% of**all graduating seniors based on the results of a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam.**For a medical study a researcher wishes to select people in**the middle 60% of the population based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation is 8, find the upper and lower reading that would qualify a person to be in the study.**In the 2008 Wimbledon tennis tournament, Rafael Nadal**averaged 115 miles per hour (mph) on his first serves. Assume that the distribution of his first serve speeds is Normal with a mean of 115 mph and a standard deviation of 6 mph. About what proportion of his first serves would you expect to exceed 120 mph?**What percent of Rafael Nadal’s first serves are between**100 and 110 mph? N(115, 6)**According to http://www.cdc.gov/growthcharts/, the heights**of 3 year old females are approximately Normally distributed with a mean of 94.5 cm and a standard deviation of 4 cm. What is the third quartile of this distribution?**Homework**• Worksheet (not the book problems listed)