3. Describing Data Numerically
Interpreting Standard Deviation
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The average birth weight at a hospital is 6.5lbs. with a standard deviation of 1.4lbs. What is the lowest weight which would be considered significantly high?
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Verified step by step guidance1
Step 1: Understand the concept of 'significantly high'. In statistics, a value is considered significantly high if it is more than 2 standard deviations above the mean. This is based on the empirical rule, which states that approximately 95% of data falls within 2 standard deviations of the mean in a normal distribution.
Step 2: Identify the given values in the problem. The mean (μ) is 6.5 lbs, and the standard deviation (σ) is 1.4 lbs.
Step 3: Use the formula for significantly high values: μ + 2σ. Substitute the given values into the formula. This becomes: .
Step 4: Simplify the expression by multiplying 2 by the standard deviation (1.4) and then adding the result to the mean (6.5).
Step 5: The result of this calculation will give you the lowest weight that is considered significantly high. Ensure you interpret the result in the context of the problem.
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