Try the fastest way to create flashcards
Question

# 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

Verified
Step 1
1 of 2

The 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 $61$.

## Recommended textbook solutions #### enVision Algebra 2

1st EditionISBN: 9780328931590 (1 more)Al Cuoco
3,573 solutions #### SpringBoard Algebra 2

1st EditionISBN: 9781457301537 (1 more)The College Board
3,003 solutions #### Big Ideas Math Algebra 2: A Common Core Curriculum

1st EditionISBN: 9781608408405 (2 more)Boswell, Larson
5,067 solutions #### Big Ideas Math: Algebra 2 A Common Core Curriculum

1st EditionISBN: 9781642088052Laurie Boswell, Ron Larson
5,066 solutions