Math Problem Statement
Standard deviations of 95,90,85,80,75,70,65,60,55
Solution
To clarify, are you asking for the z-scores (critical values) corresponding to specific confidence levels (such as 95%, 90%, etc.), or are you asking for the standard deviations of certain data sets? If you're referring to the z-scores used in hypothesis testing or constructing confidence intervals, I can provide the critical values.
For confidence levels, here are the approximate z-scores (or critical values) that correspond to common confidence intervals:
- 95% confidence level: z ≈ 1.96
- 90% confidence level: z ≈ 1.645
- 85% confidence level: z ≈ 1.44
- 80% confidence level: z ≈ 1.28
- 75% confidence level: z ≈ 1.15
- 70% confidence level: z ≈ 1.04
- 65% confidence level: z ≈ 0.93
- 60% confidence level: z ≈ 0.84
- 55% confidence level: z ≈ 0.76
These z-scores represent how many standard deviations away from the mean a certain percentage of data falls, assuming a normal distribution.
Would you like to explore any specific applications of these values or ask further questions about their use? Feel free to clarify or expand the question!
Here are 5 related questions:
- How are z-scores used to calculate confidence intervals?
- What is the relationship between standard deviation and confidence intervals?
- How do you calculate the sample size for a desired confidence level?
- What is the formula for converting a z-score to a confidence interval?
- What is the difference between z-scores and t-scores in hypothesis testing?
Tip: The critical z-value is key when constructing confidence intervals and determining the margin of error in statistics.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Z-Scores
Standard Deviation
Formulas
Z-score = (X - μ) / σ
Confidence Interval = X̄ ± Z * (σ/√n)
Theorems
Empirical Rule
Central Limit Theorem
Suitable Grade Level
Grades 10-12, College
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