Download The percentile is the % of data less than a given

Recall:
The percentile is the % of data less than a given
value (e.g. Z‐score).
The Z­score of a value is the number of standard deviations that a value is away from the mean.
Z = ­0.37 corresponds to being 0.37 σ to the left of the mean.
Apr 15­8:14 AM
Using Percentiles to
Calculate % between values
Ex: Given Q ~ N(7, 2.22), find the percent of data
in the interval 3 < q < 6.
Find Z­scores of 3 and 6
Find the corresponding percentiles for Z­scores of 3 and 6
Subtract Percentile associated with 3 from Percentile associated with 6
Z‐score for q =3,
Z‐score for q =6,
Percentile for Z = ‐1.8
Percentile for Z = ‐0.45
percentile
Subtract the percentiles to
determine the percentage between
the two z‐scores.
Therefore, 29% of the data is within the range 3<q<6
for this given distribution.
Apr 15­6:55 AM
1
You try!
Given a normal distribution of values
for which the mean is 70 and the
standard deviation is 4.5, find:
a) the percentage of values between 65 and 80.
b) the percent of values greater than 75.
c) the probability that a value is less than 62.
d) the 90th percentile for this distribution.
We want to know the X value that corresponds to the 90th percentile.
Apr 15­6:55 AM
Ex. but this time on graphing calculator
Given a normal distribution of values
for which the mean is 70 and the
standard deviation is 4.5, find:
a) the percentage of values between 65 and 80, inclusive.
normalcdf(lower,upper,mean,SD)
normalcdf(65,80,70,4.5)
b) the percent of values greater than 75.
the graphing calculator can't handle infinity ...
so the upper bound is 1 x 1099 (1 EE 99)
normalcdf(75,1x1099,70,4.5)
key in:
c) the probability that a value is less than 62.
normalcdf(‐1x1099,62,70,4.5)
key in:
d) the value which corresponds to the 90th percentile for
this distribution.
Command:
invNorm(value,mean,SD)
invNorm(0.90,70,4.5)
= 75.77
Compare the values computed using the graphing calculator to those we calculated using the Z­score tables. Which one is more accurate?
Apr 15­8:27 AM
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Computing Z‐Scores Using the TI‐83 Graphing Calculator
Given N(x,σ2):
To determine the percentage of total data
between two numbers a and b,(a < x < b):
Note: a can be ‐1x1099 for ‐infinity
b can be +1x1099 for +infinity
1) access the normalcdf function
normalcdf(a,b,μ,σ)
2) enter relevant data
3) multiply computed value by 100%
To determine the value of the nth percentile
1) access the invNorm function
2) enter relevant data
invNorm(n,μ,σ)
Graphing calc
HW: pg 186
Do with one method, verify with the other.
# 9, 10, 12, 13, 14, 15, 17
Oct 26­5:23 PM
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