Math chapter 2
In a normal distribution what percent of the values lie above the mean?
50%
In a normal distribution what percent of the values lie below the mean?
50%
In a normal distribution what percent of the values lie within one standard deviation of the mean? 1st value
68% (1st value)
In a normal distribution what percent of the values lie within two standard deviations above the mean? 2nd value
95% (2nd value)
In a normal distribution what percent of the values lie within three standard deviations of the mean?
99.7% (3rd value)
What does a curve that is equal on both sides and resembles a hill called?
A symmetric density curve. It should always have an area of 1 and follow the 68, 95, 99.7 rule.
If you see the word find a percentile and cumulative relative frequency graph what are you looking for?
A value on the vertical axis.
If you see the word PERCENTILE, see CUMULATIVE RELATIVE FREQUENCY GRAPH, and see MORE THAN, what do you need to do.
Calculate the percentage below in order to determine the percentage above. The percentage above (more than) is what you're looking for. You would subtract the percentage you got from 1 to determine the value above
Where does the mean on a curve sketch go?
In the center. The mean is the balancing point
If a graph is normally distributed and you're given a mean, a standard deviation, and it asks for a percentage, what steps must you take?
1.)Write out N (mean, standard deviation) 2.) sketch out curve with mean and given value 3.) shade what it's asking for, more than, less than, between etc 4.) NDCF (low, high, mean, StDev) 5.) find percentage and round
What does proporiton stand for?
% (percent)
Under a Normal distribution curve what is true?
-The mean is always equal to the median for any normal distribution -The area under a normal curve is always 1-regardless of the mean or standard deviation
What do you need to remember about cumulative relative frequency graphs?
-These are the graphs where you have to draw lines that connect at an intersecting point -the vertical side is the side that represents PERCENTAGES -The bottom represents values
When given a scenario that mentions a NORMAL DISTRIBUTION, A MEAN, and A STANDARD DEVIATION, and provides TWO NUMBERS with a "between" descriptor, what kind of problem is this? And what are the steps.
It is an NCDF Problem which means you do: 1.) N (Mean, StDev.) 2.) Sketch a curve (Paying attention to the fact that it says BETWEEN so you only shade the area between the numbers given (16 and 16.1)-so it would be the area between 16 and the mean) 3.) NCDF (lowest number given from the final values [16.0], highest number from the given values [16.1], Mean [16.1], Standard Deviation [0.1]) 4.) Calculator- 2nd Vars, 2, enter values) Get final answer and that is the percent.
What does standard deviation tell us?
It tells us how sprawl out the data is (Distance between one value and another)
When given values that look complex like (0<x<2) what does that indicate
It's just saying that the density curve given ranges on a scale of 0-2.
When you see the words STANDARD NORMAL DISTRIBUTION and you're only given one value what do you need to remember, and what kind of problem is this?
Mean=0 StDev=1 This is an NCDF Problem NOT an Inverse Norm
When it says between something what should you do in terms of a density curve
Put the two numbers on the curve and shade the area in between.
What does the median represent EVEN THOUGH IT DOESN'T APPEAR ON A GRAPH SKETCH?
The median represents the equal area point
What should you pay close attention to in a word problem?
What it's asking for, NOT just how to solve it
How to find the base of two values that make up one area (Ex: 0.5-1.2)
You subtract the larger value from the lesser one 1.2-0.5=.7
