STT EXAM 2 STUDY SET QUESTIONS
WITH 100% CORRECT ANSWERS
What is the empirical rule? - Answer- A shortcut rule for normal distributions: 68%, 95%,
99.7% within 1, 2, 3 standard deviations
When should you NOT use empirical rule? - Answer- When exact probabilities are
required; use calculator instead
What does symmetry of normal curve mean? - Answer- The left and right sides of the
mean are mirror images, so probabilities are equal
What is the total area under a normal curve? - Answer- 1, representing 100% of all
possible values
How do you find right tail probability? - Answer- 1 minus the left tail probability
What does a large z-score (like 3) indicate? - Answer- The value is far from the mean
and is very unusual in the distribution
Why can z-scores compare different tests? - Answer- Because they remove units and
scale everything based on standard deviations
What is mean in a normal distribution? - Answer- The center point where the distribution
balances
What is standard deviation? - Answer- A measure of how spread out the data is around
the mean
What happens to curve if SD increases? - Answer- The curve becomes wider and flatter
because data is more spread out
What happens if SD decreases? - Answer- The curve becomes narrower and taller
because data is more concentrated
What are degrees of freedom? - Answer- n − 1; reflects how much independent info is in
sample
, What is t-distribution? - Answer- A distribution similar to normal but with heavier tails for
small samples
What happens to t as n increases? - Answer- It approaches the normal distribution
What increases SE (mean)? - Answer- Larger standard deviation or smaller sample size
What decreases SE (mean)? - Answer- Larger sample size
Condition for mean CI - Answer- Sample size ≥ 30 or population is approximately
normal
Correct SE interpretation - Answer- Average distance between sample mean and
population mean across samples
Correct CI interpretation (mean) - Answer- We are X% confident the true mean lies in
the interval
z-score formula - Answer- (x − μ) / σ; measures how many standard deviations a value
is from the mean so you can compare across different distributions
What does a z-score tell you? - Answer- It tells you how unusual a value is relative to
the mean; bigger absolute value = more unusual
What does z = 0 mean? - Answer- The value is exactly equal to the mean of the
distribution
What does a positive z-score mean? - Answer- The value is above the mean, and the
number tells how far above in standard deviations
What does a negative z-score mean? - Answer- The value is below the mean, and the
number tells how far below in standard deviations
Why are z-scores useful? - Answer- They standardize different distributions so you can
compare performances across different scales
What is the standard normal distribution? - Answer- A normal distribution with mean 0
and standard deviation 1 used for z-score calculations
What does normalcdf do? - Answer- It calculates the probability (area) under a normal
curve between two values
When do you use normalcdf? - Answer- When asked for probability or percent of data
within or beyond certain values
What does invNorm do? - Answer- It finds the value (cutoff) corresponding to a given
percentile or area
WITH 100% CORRECT ANSWERS
What is the empirical rule? - Answer- A shortcut rule for normal distributions: 68%, 95%,
99.7% within 1, 2, 3 standard deviations
When should you NOT use empirical rule? - Answer- When exact probabilities are
required; use calculator instead
What does symmetry of normal curve mean? - Answer- The left and right sides of the
mean are mirror images, so probabilities are equal
What is the total area under a normal curve? - Answer- 1, representing 100% of all
possible values
How do you find right tail probability? - Answer- 1 minus the left tail probability
What does a large z-score (like 3) indicate? - Answer- The value is far from the mean
and is very unusual in the distribution
Why can z-scores compare different tests? - Answer- Because they remove units and
scale everything based on standard deviations
What is mean in a normal distribution? - Answer- The center point where the distribution
balances
What is standard deviation? - Answer- A measure of how spread out the data is around
the mean
What happens to curve if SD increases? - Answer- The curve becomes wider and flatter
because data is more spread out
What happens if SD decreases? - Answer- The curve becomes narrower and taller
because data is more concentrated
What are degrees of freedom? - Answer- n − 1; reflects how much independent info is in
sample
, What is t-distribution? - Answer- A distribution similar to normal but with heavier tails for
small samples
What happens to t as n increases? - Answer- It approaches the normal distribution
What increases SE (mean)? - Answer- Larger standard deviation or smaller sample size
What decreases SE (mean)? - Answer- Larger sample size
Condition for mean CI - Answer- Sample size ≥ 30 or population is approximately
normal
Correct SE interpretation - Answer- Average distance between sample mean and
population mean across samples
Correct CI interpretation (mean) - Answer- We are X% confident the true mean lies in
the interval
z-score formula - Answer- (x − μ) / σ; measures how many standard deviations a value
is from the mean so you can compare across different distributions
What does a z-score tell you? - Answer- It tells you how unusual a value is relative to
the mean; bigger absolute value = more unusual
What does z = 0 mean? - Answer- The value is exactly equal to the mean of the
distribution
What does a positive z-score mean? - Answer- The value is above the mean, and the
number tells how far above in standard deviations
What does a negative z-score mean? - Answer- The value is below the mean, and the
number tells how far below in standard deviations
Why are z-scores useful? - Answer- They standardize different distributions so you can
compare performances across different scales
What is the standard normal distribution? - Answer- A normal distribution with mean 0
and standard deviation 1 used for z-score calculations
What does normalcdf do? - Answer- It calculates the probability (area) under a normal
curve between two values
When do you use normalcdf? - Answer- When asked for probability or percent of data
within or beyond certain values
What does invNorm do? - Answer- It finds the value (cutoff) corresponding to a given
percentile or area
