The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the probability that a student will score more than 1700 points?

Question

3115 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-16T03:13:01

The Probability that a student will score more than 1700 points $=0.5$

The Mean Score is $=1700$
Standard deviation is $=75$

The $z$ score corresponding to mean score $1700= (x-barx)/sigma=(1700-1700)/75=0$

$z$ score corresponds to $1700$ is $=0$

The area $> 1700$ lies to the right of $z=0$

The required probability is given by the area between $z=0$ and $z=oo$

This area represents $0.5$

The Probability that a student will score more than 1700 points $=0.5$

Look at the image

It could be easily found like this-

The values are normally distributed. The Probability of the area under Normal Curve represents $=1$

Values greater than 1700 represents one-half of the area. The right wing of the normal curve represents values > 1700, hence probability $0.5$