Stat2Lab4

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University of California, Berkeley *

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201A

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Statistics

Date

Feb 20, 2024

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pdf

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Stat 2 Lab #4: Standard Units and the Normal Curve Learning objectives: • Compare histograms and normal approximations to them, including axes. • Convert back and forth between original units and standard units • Understand basic facts about the normal curve • Calculate areas under the normal curve for specified intervals • Approximate the percent of observations in an interval using the normal approximation 1. In the HANES5 study, men age 18 and over had an average height of 69 inches and an SD of 3 inches. The histogram is shown below, with a normal curve. Fill in the blanks below. For (a), (b), (d) and (e), choose from: [66 inches], [72 inches], [- 1], [+1]. For (c) and (f), choose from: [normal curve], [histogram]. The percentage of men with heights between 66 inches and 72 inches is exactly equal to the area between (a) __ and (b) __ under the (c) __ . This percentage is approximately equal for the area between (d) __ and (e) __ under the (f) __ . Emily Gimenez - -- ble 72 histogram - 1 + normal Curve 666972

2. Use the normal table to find the areas of each of the shaded regions under the normal curves below. If the value you need is in between two values in the table, use the value that is closest. . − 1.58 0.00 1.70 0.00 1.06 0.00 0.78 1.60

3. A teacher wants to evaluate how fast her 8th grade students are able to type. She has them all take the same typing speed test and finds that the average speed is 15 words per minute, with a standard deviation of 4 words per minute. She makes a histogram of the speeds, and this approximately follows the normal curve. Use the normal approximation to find the percentage of her students who type between 10 and 20 words per minute. 4. Among the students who took STAT 2 one semester, the average midterm score was about 84, the SD was about 5, and the highest score was 90. Did the midterm scores follow the normal curve? Explain briefly.

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