Question

SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming that this scaling still applies, use a calculator or online z-score calculator, to find the probability that a randomly selected SAT student scores morethan 620.

Answer 1

Solution

Step 1:

Given data:

$\begin{gathered} Mean\text{ }\mu\text{ = 500} \\ Standard\text{ deviation }\sigma\text{ = 100} \\ \text{x = 620} \end{gathered}$

Step 2:

Find the z-score

$\begin{gathered} z-score\text{ = }\frac{x\text{ - }\mu}{x} \\ z-score\text{ = }\frac{620\text{ - 500}}{100} \\ z-score\text{ = }\frac{120}{100} \\ z-score\text{ = 1.2} \end{gathered}$

Step 3

Determine the probability that a randomly selected SAT student scores more

than 620 by finding the z-score of 1.2 from the z score table.

= 1 - 0.8849

= 0.1151

= 11.5%

Final answer

Option D

11.5%