A newspaper article reports that the mean math score on SAT was 500 and 20% of students scored below 430.?

Question

Assume a normal distribution.

a) Find standard deviation of the math SAT scores

b) Find % of students whose math scores were above 520

Answer 1

the formula for changing from the standard normal to any other normal random variable with mean μ and standard deviation σ is:

X = μ + Z * σ

we know from the standard normal that P(Z < z) = 0.20 when z = -0.8416212

we have:

430 = 500 - 0.8416212 * σ

σ = (430 - 500) / -0.8416212 = 83.17281

Find P( X > 520 )

P( ( X - μ ) / σ > ( 520 - 500 ) / 83.17281 )

= P( Z > 0.2404632 )

= P( Z < -0.2404632 )

= 0.4049856