2.2 Normal Curves Flashcards
How can I find a percentile if all I have is a mean and s.d.?
Assuming the distribution is normal, just use normalcdf. Sketch the curve if you need to show your work.
How do I find the area under a normal curve between z = -0.8 and z = 1.2?
normalcdf (lower = -0.8, upper = 1.2, mean = 0, s.d. = 1)
What is the standard normal curve?
A normal curve with mean = 0 and s.d. = 1. The x-values are just z-scores.
For a normal distribution, how could I approximate which two numbers have 95% of the data between them?
68-95-99.7 rule. 95% of the data is within two s.d.’s of the mean. So just take the mean and subtract two s.d.’s from it for the lower number and add them for the upper number.
For a normal distribution, what range of x-values would have only 5% of the data outside of it?
The same as would have 95% within it. 2 s.d.’s below the mean to 2 s.d.’s above the mean.
When do I want to use invnorm on the calculator?
When you know a percentage and you want a specific data value. Ex: what test score is at the 90th percentile/
What is a density curve?
A theoretical curve that would contain all of the possible data. It’s like making a histogram but with an infinite amount of data so it’s a smooth curve instead of bars.
How do I find percentages/proportions from a density curve?
The area underneath the curve between any two points is the percentage of data between those points. The total area is always 1 (100% of the data).
If all I have is summary statistics, how can I tell if the data is approximately normal?
You can’t make a very good conclusion about shape without more information. However, the mean and median should be approximately equal to each other. If they aren’t very close, that would be a good indication that the data isn’t normal.
If all I have is a graph (dotplot, histogram, etc), how can I tell if the data is approximately normal?
Say that the distribution of (context) is roughly symmetric, therefore approx. normal. Or that it (with context) is skewed or has outliers and therefore not normal.
If I have a normal probability plot, how can I tell if the data is approximately normal?
If the normal probability plot is roughly linear, then the data is approximately normal.
If a normal probability plot is curved, how can I tell which way the data is skewed?
Picture all the data falling to the x-axis. If the “pile” is on the left, the data is right-skewed and vice-versa.
In a density curve, how can I approximate the mean and median?
The median is the equal-area point and the mean is the balancing point. More important: the mean will always be pulled in the direction of any skew (when compared to the median).
How do I use normalcdf to find the percent of data above a certain value?
Use that value as the lower bound and type a big number (999999) as the upper bound. normalcdf(value, 999999, mean, s.d.)
