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?

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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#