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 from the problem. The mean (μ) is 6.5 lbs, and the standard deviation (σ) is 1.4 lbs.
Step 3: Use the formula to calculate the threshold for significantly high values: μ + 2σ. This formula adds 2 standard deviations to the mean to determine the lowest value that would be considered significantly high.
Step 4: Substitute the given values into the formula. Replace μ with 6.5 and σ with 1.4, resulting in the expression: 6.5 + 2(1.4).
Step 5: Simplify the expression to find the threshold. This will give you the lowest weight that is considered significantly high. Note: Do not calculate the final value as per the instructions.
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