Describing Location
The definition of a percentile
Specific locations in a distribution
Most commonly used density curve
Normal curve
The area under the curve that is less than 7.2, following a standard normal curve
0.53 or 53%
When to use Normalcdf
Given z-score or an x-value and want to find percentile or area under the curve
When there is more than one transformation, you follow this
Order of Operations
Uses mean and standard deviation to standardize any score
Z-Score
Characteristics of a density curve
- On/above the horizontal axis
- Area under the curve = 1
- Does not need to curve
Harry got an 88 on his stats test that had a mean of 83 with a standard deviation of 7. If the scores are normally distributed, what percent of students scored lower than Harry?
76.2%
When to use InvNorm
If given area under the curve or percentile and want to find z-score or x-value
Adding or Subtracting
Center: inc/dec
Spread: no change
Shape: no change
Another term for a Cumulative Relative Frequency Graph
Ojive
Normal curve notation
N(u,o)
u: mean of population/model
o: standard deviation of population/model
about 62%
What the Normal Probability Plot tells us
Whether or not we can use normal calculations / if something follows a normal distribution
Multiplying or Dividing
Center: inc/dec
Spread: inc/dec
Shape: no change
When 2 observations have the same value
They're at the same percentile
68, 95, 99.7
Empirical Rule
The top 10% of scores on the PSAT receive small college scholarships, if PSAT scores are normally distributed and the mean is 120 with a standard deviation of 17, what score is needed to be eligible for the scholarship?
142
Mention this when assessing normal
- if the mean and median are roughly equal
- if the area under the x-axis = 1
- if you make a box plot
- normal probability plot results
Sample values that fall very far away from the vast majority of other sample values.
outliers
Formula to find the percentile
Below/Total
Characteristics of a Normal Curve
- Symmetrical distribution
- Unimodal
- Mean and median both lie at center
The average yearly snowfall in Chillyville is approximately Normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation?
4.83 inches
Sketch a normal probability plot, one that is right-skewed, and one that is left-skewed
normal: linear
A measure of the amount that the data values vary among themselves
variation