A certain standardized test\'s math scores have a bell-shaped distribution with

Question

A certain standardized test's math scores have a bell-shaped distribution with a mean of 520 and a standard deviation of 114. Complete parts (a) through (c).

(a) What percentage of standardized test scores is between 178and 862?

__% (Round to the nearest tenth as needed.)

(b) What percentage of standardized test scores is less than 178or greater than 862?

__% (Round to the nearest tenth as needed.)

(c) What percentage of standardized test scores is greater than 748?

__% (Round to the nearest tenth as needed.)

Explanation / Answer

mean = 520

standard deviation = 114

a)

z value for 178 is (178-520)/114 = -3, correspoding p value using z-table is 0.00135

P(score<178) = 0.0013

z value for 862 is (862-520)/114 = 3, correspoding p value using z-table is 0.9987

P(score<862) = 0.9987

P(178<score<862) = 0.9987 -0.0013 = 0.9974

percentage of standardized test scores is between 178and 862 = 99.7%

b)

P(score<862) = 0.9987

P(score>862) = 1-0.9987 = 0.0013

P(sore<178 or score>862) = 0.0013+0.0013 =0.0026

percentage of standardized test scores is less than 178or greater than 862 = 0.3%

c)

z score for 748 is (748-520)/114 = 2 ,correspoding p value using z-table is 0.9772

P(score<748) = 0.9772

P(score>748) = 1-0.9772 = 0.0228

percentage of standardized test scores is greater than 748 = 2.3%

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