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?
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: [tex]z=\frac{X-\mu}{\sigma}[/tex] Plugging the given values into the formula, we get: [tex]-0.44=\frac{X-21.3}{6.2}[/tex] Solving for X, gives X = 18.572. Therefore Vince's score < 18.572.
