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

z

-3 -2 -1 0 1 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

z

-3 -2 -1 0 1 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

having weights:

• less than 4.0 kg

• more than 4.0 kg

• between 3.0 kg and 4.0 kg