Answer:
24.24
Explanation:
Sarah's composite score is the score such that:
P(X≤x) = 0.85
It means that the probability that a score will be lower than Sarah's score is 0.85.
But we have the standardized normal distribution table, so we first, will find a z such that:
P(Z≤z) = 0.85
Using the table, the closest number to 0.85 is 0.8508, so the value of z is 1.04.
1.0 from the row added to 0.04 from the column.
Now, x and z are related as:
[tex]z=\frac{x-m}{s}[/tex]
Where m is the mean and s is the standard deviation. So, replacing z by 1.04, m by 18, and s by 6, we get:
[tex]1.04=\frac{x-18}{6}[/tex]
So, solving for x, we get:
[tex]\begin{gathered} 1.04\cdot6=\frac{x-18}{6}\cdot6 \\ 6.24=x-18 \\ 6.24+18=x-18+18 \\ 24.24=x \end{gathered}[/tex]
Therefore, Sarah's composite score is 24.24
