Question

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Question :

On a certain standardized test

• The mean is 51
• The standard deviation is 15

Exactly 66% of the people who took the test scored higher than Mr. Peterson. Find a, b, and c such that Mr. Peterson's score is approximately

a + b ⋅ Φ^c(d)

Do not make a continuity correction.

What is a + b + 2bcd?

X is a random person’s score. X is approximately Normal(51,15²).

x = Mr. Peterson’s score.

P(X > x) = 0.66

P((X − 51)/15 > (x − 51)/15) = 0.66          normalize

P(Z > (x − 51)/15) ≈ 0.66                            approximate

1 − P(Z > (x − 51)/15) ≈ 1 − 0.66

P(Z ≤ (x − 51)/15) ≈ 0.34

?((x − 51)/15) ≈ 0.34

(x − 51)/15 ≈ ?⁻¹(0.34)

x ≈ 51 + 15 ?⁻¹(0.34)

Answer 1

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a+b+2bcd = 51+15+2*15*-1*0.34 = 55.8