Download Notes #11 : 68 – 95 – 99

68 – 95 – 99.7 Rule
Name:__________________________
1) In a Normal Distribution, 68% of the Data falls within one standard deviation of the mean. So that would be between Z
scores z = 1 and z = -1
2) In a Normal Distribution, 95% of the data falls within 2 standard deviations of the mean. So that would be between Z
scores of z = 2 and z = -2
3) In a Normal Distribution, 99.7% (almost 100!) of the data falls within 3 standard deviation of the mean. So that
would be between Z scores of z = 3 and z = -3.
Examples:
1) Find the mean and the standard deviation for the normal distribution described by the curve shown in the figure.
a) Mean = _____________
b) Standard Deviation = _____________
2) Find the mean and the standard deviation for the normal distribution described by the curve shown below in the picture
a) Mean = ________________
b) Standard Deviation = ____________________
Percentiles and a Normal Distribution
SAT Scores: What we are dealing with here are SAT scores that have a normal distribution with a mean of 500 and a
standard deviation of 100.
a) Label a picture that represents this Normal Distribution. (Include percents we learned from the 68 -95 – 99.7 Rule)
b) If I have a score of 600, what percent of students scored higher than me? ____________________
What percentile is that? ________________
c) What if I had a score of 680, what percent of students scored higher than me? Not so easy, huh?
The first thing we want to do to figure this out is to find our Z – Score. Do that real quick using your z = formula on your
purple sheet.
Now look at your Table of Normal Percentiles. 1) Look on the left hand column for the first two digits (1.8)
2) Look on the Top column for the third digit (.00)
3) Where the row and column intersect is the number we are looking for.
What is that number? ___________ Change this to a percent and that is your percentile.
d) What percentile is a student in who scored a 480 on their SAT?
e) What percentile is a student in who scored a 560 on their SAT?
What about the other way around?
a) What score does a student have who is in the 68th percentile?
~Find .68 on your table…then find its Z-Score
~Use your X = formula to find the data point
b) What score does a student have who is in the 37th percentile?