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The GRE is an entrance exam that most students are required to take upon entering graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12. What percent of scores were between 286 and 322? Round your answer to the nearest whole number.

Respuesta :

asher125
Yes i believe the answer is 289
JeanaShupp

Answer: [tex]82\%[/tex]

Step-by-step explanation:

Given: Mean [tex]\mu= 310[/tex]

Standard deviation [tex]\sigma =12[/tex]

The formula for z score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 286

[tex]z=\dfrac{286-310}{12}\\\\\Rightarrow\ z=-2[/tex]

P value of (z=-2 )=0.0228

For x= 322

[tex]z=\dfrac{322-310}{12}\\\\\Rightarrow\ z=1[/tex]

P value of (z=1)= 0.8413

Now, the probability of students score between 286 and 322 is given by :-

[tex]P(286<x<322)=0.8413-0.0228=0.8185\approx0.82=82\%[/tex]

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