Empirical Rule Basics
What percentage of data falls within one standard deviation of the mean in a normal distribution?
68%
What does a z-score tell you?
How many standard deviations a value is from the mean
Label the center of the curve.
μ (mean)
What menu do you use to find summary statistics for a column?
Stat → Summary Stats → Columns
What does the Central Limit Theorem say about sampling distributions?
As n increases, the sampling distribution of the mean becomes normal
What percentage of data falls within two standard deviations?
95%
If z = 0, where are you on the curve?
At the mean
Label the first tick mark to the right of the mean.
μ + 1σ
Which menu lets you find area under a normal curve?
Stat → Calculators → Normal
What symbol represents the mean of the sampling distribution?
μₓ̄ = μ
What percentage of data falls within three standard deviations?
99.7%
What’s the area to the left of z = 0?
0.5 (50%)
Label the area that contains 34% of the data.
Between μ and μ + 1σ (or μ - 1σ)
How do you find a z-score for a value in StatCrunch?
Use Stat → Calculators → Normal, enter μ and σ, then adjust “P(X < value)”
What happens to σₓ̄ as sample size increases?
It decreases
If a distribution has a mean of 100 and σ = 10, what range contains 68% of the data?
90 to 110
A z-score of 2.0 corresponds to what percentile (approx.)?
97.5th percentile
Label the area that contains 13.5% of the data.
Between μ + 1σ and μ + 2σ (and symmetrically on the left)
How do you find a confidence interval for a mean in StatCrunch?
Stat → T Stats → One Sample → With Data (or Summary)
What confidence level corresponds to z = 1.96?
95%
If 95% of the data are between 60 and 100, what are the mean and standard deviation?
Mean = 80, σ = 10
If a student’s test score has z = -1.2, what percentage scored higher?
About 88.5%
What small percentage of data lies beyond μ + 3σ?
0.15%
How do you use StatCrunch to perform a hypothesis test for a population mean?
Stat → T Stats → One Sample → With Data/Summary → enter μ₀ → select alternative hypothesis
A 95% confidence interval for μ is (80, 100). What does that mean?
We’re 95% confident the true mean lies between 80 and 100