Uniform & Normal Basics
What kind of probability distribution has equally likely outcomes across all intervals?
Uniform distribution
What percent of data falls within 1 standard deviation of the mean?
68%
The area under the curve represents what two interpretations?
Proportion of the population and probability
Which calculator in StatCrunch is used to find probabilities for the normal curve?
Stat → Calculators → Normal
If heights are normally distributed with μ = 55.9 and σ = 5.7, what proportion of 10-year-old boys are taller than 62 inches?
Area to the right of 62
What is the total area under any probability density curve?
1
What percent of data falls within 2 standard deviations?
95%
The area to the right of x = 200 in the cholesterol example was 0.2903. What does this mean?
29.03% of males have cholesterol above 200
What are the default parameters for the z-curve in StatCrunch?
Mean = 0, SD = 1
What percentile is a boy at if he’s 45 inches tall?
Left-tail percentile
What happens to a normal curve when you increase the mean?
The curve shifts horizontally
What percent of data falls within 3 standard deviations?
99.7%
If the total area under the curve is 1, what’s the area to the left of the mean?
0.5
How do you find P(X ≥ value)?
Use “above” option in the calculator
What height corresponds to the 95th percentile?
Use inverse percentile calculation
What happens to a normal curve when you increase the standard deviation?
It flattens and spreads out
If μ = 180 and σ = 36.2, between what values is 68% of the data?
143.8 to 216.2
If the area between 180 and 216.2 is 34%, what’s the area below 180?
50%
How do you find a percentile?
Use “between” or “below” and adjust until area matches
What proportion of IQ scores are between z = -1 and z = 1?
68%
At what points are the inflection points on a normal curve?
μ − σ and μ + σ
Beyond μ + 3σ, how much area remains in the tail (on one side)?
0.15%
A value is at the 90th percentile. What proportion is below it?
0.90
What must you always label on a drawn normal curve?
Mean and at least ±1, 2, 3 SD
If 98% of oil changes take less than t minutes, what does t represent?
98th percentile (or cutoff time)