Question

HW Score: 23 33%, 7 of 30 Question Help Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 568 and a standard deviation of 112. Use the 68-95-997 Rulete find the percentage of people taking the test who score below 232 The percentage of people taking the test who score below 232 is %

Answer 1

Given mean of the scores(M)= 568

Standard deviation

() = 112

According to 68-95-99.7 rule:

$Pr(M-\sigma\leq X \leqM+\sigma)=0.68$

$Pr(M-2\sigma\leq X \leqM+2\sigma)=0.95$

$Pr(M-3\sigma\leq X \leqM+3\sigma)=0.997$
Pr stands for probability
Here 0.68 implies 68%, 0.95 implies 95% and 0.997 implies 99.7%

We need to find the percentage of people scoring below 232

568-(3*112)=232

568+(3*112)=904

this falls in the third interval which can be expressed as:

$Pr(232\leq 568 \leq 904)=0.997$

this implies that the probability of scoring more than 904 or less than 232 $Pr(232<X \cap X>568)=1-0.997=0.003$ Here 0.003 corresponds to 100-99.7=0.3%
Considering equal percentage of people below 232 and above 904,

THE PERCENTAGE OF PEOPLE SCORING BELOW 232 is (0.3/2)=0.15%