Transcript Thinking Mathematically by Robert Blitzer

Thinking
Mathematically
Statistics:
12.5 Problem Solving with the Normal Distribution
Percentiles
If n% of the items in a distribution are less
than a particular data item, we say that the
data item is in the nth percentile of the
distribution.
For example, if a student scored in the 93rd
percentile on the SAT, the student did better
than about 93% of all those who took the
exam.
Percentiles and z-scores
• Table 12.14 in the text relates z-scores to percentiles.
• To determine the percent below a value, compute the zscore and look-up the corresponding percentile in table
12.14
• To determine the percent above, compute z-score, look-up
percentile, and subtract from 100
• To determine the percent between two values, compute
both z-scores, look-up percentiles, and subtract.
 What % falls between z values of -1, +1? -2, +2? -3, +3?
The 68-95-99.7 Rule for the Normal Distribution
99.7%
95%
68%
-3
-2
-1
1
2
3
Examples: Percentiles
Exercise Set 12.5 #7, 11
•
Find the percentage of data items in a normal
distribution that
a) Lie below a z score of -1.2
b) Lie above a z score of -1.2
•
Find the percentage of data items in a normal
distribution that lie between z = 1 and z = 3.
Examples: Percentiles
Exercise Set 12.5 #19, 25
Systolic blood pressure readings are normally
distributed with a mean of 121 and a standard
deviation of 15.
• Find the percentage of readings above 130.
• Find the percentage of readings between 112
and 130.
Thinking
Mathematically
Statistics:
12.4 The Normal Distribution