Hw6_24

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Statistics

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Jul 2, 2024

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NAME: STAT:1010 Statistics and Society Instructor: Osnat Stramer HOMEWORK 6 Submit your work as a single file to Canvas/ICON. Please check that your work is readable. Section 5.2: questions 18, 20, 24,38, 40, In addition to the textbook questions answer the following questions 1. The average wind speed in San Francisco in July is 13.6 miles per hour (mph), according to the U.S. National Oceanic and atmospheric Administration. Suppose that the distribution of the wind speed in July in San Francisco is normal, with mean μ = 13.6 mph and standard deviation σ = 4. a. Sketch and label the distribution of wind speed in July in SF. Include the data scale, the standard scale, and the 68-95-99.7 Rule labels. b. Approximate the percentage of time the wind speed is between 9 mph and 18 mph. c. Do you think a wind speed of 10 mph is unusual? Explain d. Approximate the percentage of time the wind speed is over 20 mph. e. What is the z -score for a gust of wind measuring 35 mph? Is this wind speed unusual? 2. The state of Georgia reports that the mean temperature statewide for the month of April is μ = 61.5°F. Assume that the standard deviation is σ = 8°F and that temperature in Georgia in April is normally distributed. Draw the normal curve for temperatures between 45.5°F and 77.5°F. Find the probability that the temperature is between 45.5°F and 77.5°F in April in Georgia. 3. The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. a. What is the z -score for a woman 6 feet tall? b. What is the z -score for a man 6 feet tall? c. Which is more unusual, a man shorter than 5 feet, 5 inches tall or a woman over 6 feet, 1 inch tall? Explain!

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