A sample of 500 random adult books in a library has an average of 312 pages with a standard deviation of 26 pages. According to the Empirical Rule of Standard Deviation, find the central range of page lengths containing 95% of the books in the sample.
Table of contents
- 1. Introduction to Statistics53m
- 2. Describing Data with Tables and Graphs2h 2m
- 3. Describing Data Numerically2h 8m
- 4. Probability2h 26m
- 5. Binomial Distribution & Discrete Random Variables3h 28m
- 6. Normal Distribution & Continuous Random Variables2h 21m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 37m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - ExcelBonus23m
- Introduction to Confidence Intervals22m
- Confidence Intervals for Population Mean1h 26m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - ExcelBonus28m
- Confidence Intervals for Population Means - ExcelBonus25m
- 8. Sampling Distributions & Confidence Intervals: Proportion2h 20m
- 9. Hypothesis Testing for One Sample5h 15m
- Steps in Hypothesis Testing1h 13m
- Performing Hypothesis Tests: Means1h 1m
- Hypothesis Testing: Means - ExcelBonus42m
- Performing Hypothesis Tests: Proportions39m
- Hypothesis Testing: Proportions - ExcelBonus27m
- Performing Hypothesis Tests: Variance12m
- Critical Values and Rejection Regions29m
- Link Between Confidence Intervals and Hypothesis Testing12m
- Type I & Type II Errors16m
- 10. Hypothesis Testing for Two Samples5h 35m
- Two Proportions1h 12m
- Two Proportions Hypothesis Test - ExcelBonus28m
- Two Means - Unknown, Unequal Variance1h 2m
- Two Means - Unknown Variances Hypothesis Test - ExcelBonus12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - ExcelBonus9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - ExcelBonus21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - ExcelBonus12m
- Two Variances and F Distribution29m
- Two Variances - Graphing CalculatorBonus15m
- 11. Correlation1h 24m
- 12. Regression3h 42m
- Linear Regression & Least Squares Method26m
- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - ExcelBonus8m
- Finding Residuals and Creating Residual Plots - ExcelBonus11m
- Inferences for Slope32m
- Enabling Data Analysis ToolpakBonus1m
- Regression Readout of the Data Analysis Toolpak - ExcelBonus21m
- Prediction Intervals13m
- Prediction Intervals - ExcelBonus19m
- Multiple Regression - ExcelBonus29m
- Quadratic Regression23m
- Quadratic Regression - ExcelBonus10m
- 13. Chi-Square Tests & Goodness of Fit2h 31m
- 14. ANOVA2h 32m
3. Describing Data Numerically
Interpreting Standard Deviation
Multiple Choice
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? Hint: Range Rule of Thumb - Numbers which are 2 or more standard deviations away from the mean are considered "significant".
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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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