Question

Vince's 2011 act reading score was below 33% of all the scores. if the mean and standard deviation for all act reading scores in 2011 were 21.3 and 6.2 respectively, what was vince's score?

Answer 1

The z-score corresponding to a cumulative probability of 0.33 is -0.44.
Let X be the score just above Vince's highest possible score.
The required formula is:

`z=(X-\mu)/(\sigma)`
Plugging the given values into the formula, we get:

`-0.44=(X-21.3)/(6.2)`
Solving for X, gives X = 18.572.
Therefore Vince's score < 18.572.