Download Day 8 Non-Standard Normal Distribution

Non-standard Normal
Distribution
OBJ• Determine the z-score of a
non-standard normal distribution
and find its area under the normal
curve
Each data item x can be
converted to a standard value z
by the formula: z = x – x
s
EX: The mean and
standard deviations of
the algebra test
scores are as follows:
• Class 1: mean =
78.4, standard
deviation  9.6
• Class 2: mean =
78.4, standard
deviation  14.5
For each class give,
the standard value of
the scores 92 and 68.
a. What percent is
between 92 and 68
for class 1?
b. What percent is
between 92 and 68
for class 2?
z
-3 -2 -1 0
1
2
3
-3 -2 -1 0
1
z
2 3
Below are the algebra test scores
for a class of 25 students:
50 64 68 70 70 72 73 75 75 76 78 78 79
80 81 82 82 82 85 88 88 89 90 92 93
z
-3 -2 -1 0
1
2
3
-3 -2 -1 0
1
z
2 3
Below are the algebra test scores
for a class of 25 students:
56 57 58 60 61 65 67 68 70 71 74 75 77
79 82 87 88 89 92 95 96 97 98 99 99
Each data item x can be
converted to a standard value z
by the formula: z = x – x
s
EX: Over the last 10
years, the mean weight x
of newborn babies in a
large metropolitan
hospital has been 3.4 kg
and the standard
deviation s has been 0.4 kg.
Find the approximate
percent of newborn babies
• less than 4.0 kg
• more than 4.0 kg
• between 3.0 kg and
4.0 kg