The Mean and Standard Deviation of Mathematics Achievement Test are 500 and 100, respectively. Find the 25th percentile rank (the score that total of 25% falls at or below)

Brenda Jordan

Brenda Jordan

Answered question

2022-11-02

The Mean and Standard Deviation of Mathematics Achievement Test are 500 and 100, respectively. Find the 25th percentile rank (the score that total of 25% falls at or below)

Answer & Explanation

Gilbert Petty

Gilbert Petty

Beginner2022-11-03Added 23 answers

MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document The random variable X is defined as Mathematics Achievement Test which follows normal distribution with mean 500, and standard deviation 100.
The 25th percentile rank is,
P ( X < x ) = 0.25 P ( X μ σ < x 500 100 ) = 0.25 P ( z < x 500 100 ) = 0.25
The probability 0.25 would be converted to z score can be obtained using the excel formula “=NORM.S.INV(0.25)”. The z score value is –0.6745.
The required value is,
P ( z < x 500 100 ) = 0.25 P ( z < x 500 100 ) = P ( z < 0.6745 )
Comparing on both sides.
x 500 100 = 0.6745 x 500 = 67.45 x = 500 67.45 = 432.55 433Thus, the 25th percentile rank is 433.

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