3. If the mean is 100 and the standard deviation is 20, then how many standard deviations above or below the mean is the value 59.1? Round to two decimal places and include the sign if below the mean. $X = \frac{59.1 - 100}{20} = -2.05$ $X = \frac{59.1 - 100}{20} = -2.05$ 4. Fill in the blanks below with percentages to describe the empirical rule for a normal distribution. The percent of area within one standard deviation above and below the mean is $68.26$%. The percent of area within two standard deviations above and below the mean is $95.44$%. The percent of area within three standard deviations above and below the mean is $99.73$%. The total percent of area under the entire normal distribution curve is equal to $100$%.
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- Mean (\(\mu\)) = 100 - Standard deviation (\(\sigma\)) = 20 - Value (\(X\)) = 59.1 Show moreā¦
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2.) Use the diagram below to illustrate a normal distribution with a mean of 100 and a standard deviation of 20 by filling in the values on the x-axis. The vertical lines denote standard deviations above/below the mean. 3.) How many standard deviations above or below the mean is the value 59.1? Round to two decimal places. 4.) Fill in the blanks to describe the empirical rule for a normal distribution. The percent of area within one standard deviation above and below the mean is ______ %. The percent of area within two standard deviations above and below the mean is ______ %. The percent of area within three standard deviations above and below the mean is ______ %.
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