## Related questions with answers

All members of the junior class at a local high school took the PSAT exam. The distribution of the results of the mathematics section was found to be approximately normal, with a mean score of 52 and a standard deviation of 6.8. Stephan claimed that he scored better than 90% of the students in the junior class. Use z-sore and your z-table to determine what score Stephan must have earned to be correct.

Solution

VerifiedThe closest value to $90$ percent is $0.8997$ and it's achieved for $z$-score $=1.28$. Now, we can find what score Stephan must have earned.

$\begin{align*} x&=z\text{-score }\cdot\text{ standard deviation }+\text{ mean}\\ &=1.28\cdot 6.8+52\\ &=60.704 \end{align*}$

Because the achieved score must be an integer, Stephan must've achieved a score greater than or equal to $61$.

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