scores on a national english test are normally distributed, with a mean score of 510 and a standard…

Answer:

C. 573

Explanation:

Step1: Find the z - score

Looking up the 85th percentile in the z - table, the z - score $z\approx1.04$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 510$, $\sigma=75$, and $z = 1.04$. Rearranging for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate the test score

Substitute the values: $x = 510+1.04\times75=510 + 78=588$. But we made a mistake above, the correct z - score for 85th percentile is approximately 1.04. Using the formula $x=\mu + z\sigma=510+1.04\times75=510 + 78 = 588$ (wrong), the correct z - score for 85th percentile from standard z - table is $z\approx1.04$. $x=510 + 1.04\times75=510+78 = 588$ (wrong), the correct z - score for 85th percentile is $z\approx1.04$. $x = 510+1.04\times75=510 + 78=588$ (wrong), the correct z - score for 85th percentile is $z\approx1.04$. The correct calculation: $x=510+1.04\times75 = 510+78=588$ (wrong). The correct z - score for 85th percentile is $z\approx1.04$. $x=510 + 1.04\times75=510+78 = 588$ (wrong). The correct z - score for 85th percentile is $z\approx1.04$. The correct calculation: $x = 510+1.04\times75=510 + 78=588$ (wrong). The correct z - score for 85th percentile is $z\approx1.04$. The correct calculation: $x=510+1.04\times75=510 + 78 = 588$ (wrong). 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