Useful Fact Sheet Chapter 7 and 8
Raw Score (Transforming a z-score into x-value): Standardized Z-Score or Standard Score:
Distribution of Z: Distribution of X: Distribution of :
Central Limit Theorem: Mean and Standard Deviation(standard error of the mean):
Standardized Z-Score for :
Empirical Rule (68 – 95 – 99.7 Rule)
• About 68% of the data lie within one standard deviation of the mean.
• About 95% of the data lie within two standard deviations of the mean.
· About 99.7% of the data lie within three standard deviations of the mean.
InvNorm (area, µ, σ) - Normal area function
area = area to the left
It returns x, where P(X < x)=area
normalcdf (lower bound, upper bound ,µ, σ) - normal probability
cumulative distribution function,
normalpdf (numtrials ,p, x) - normal probability distribution function
numtrials = number of trials,
p = probability of success, and
x is the number of successes.
Pearson’s index = A Pearson’s index greater than 1 or less than –1 indicates skewness.
Outliers for Normal Distribution: above Q3 + or below Q1 -
Normal Approximation to the Binomial:
n = # trials p=probability of success q=probability of failure=1-p r=number of successes
If np >5 and nq >5 then r has a binomial distribution that is approximated by a normal distribution with
Continuity Correction: For going from Binomial to Normal
1. If r is a left endpoint of an interval, subtract 0.5 to obtain the corresponding normal variable. x=r-0.5
2. If r is a right endpoint of an interval, add 0.5 to obtain the corresponding normal variable. x=r+0.5
c -Confidence Interval for Sample Mean (µ):
where M.E. = when σ unknown d.f. = n-1
M.E. = when σ known
c -Confidence Interval for Population Proportion (p): when
where M.E. = when and
Sampling Size for Estimating:
Means (µ):
Proportion (p): with preliminary estimate for p
with no preliminary estimate for p
For Normal Distribution / For Proportionσ is unknown / σ is known
Test Statistic / tobs / zobs
Calculator / Stat⟶Test⟶T-test / Stat⟶Test⟶Z-test / Stat⟶Test⟶
1-Prop Z-test
Confidence Interval / / /
Calculator / Stat⟶Test⟶T-Interval
Option 8 / Stat⟶Test⟶Z-Interval
Option 7 / Stat⟶Test⟶
1-Prop Z-Interval
Critical Values Zc: