The scores on a college entrance exam is 100 with a standard deviation of 7.5. How do you find the probability that a randomly selected score is between 85 and 100?

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Answer 1 · 2017-06-22T14:37:30

Proability that a randomly selected score is between #85# and #100# is #47.72%#

Asumming that the distribution is normal, let us find the #z# score of #85# and #100#.

As #mu=100# and #sigma=7.5#

#z#-score is given by #(x-mu)/sigma#

Hence for #85#, #z#-scorre is #(85-100)/7.5=-15/7.5=-2#

and for #100#, #z#-scorre is #(100-100)/7.5=0#

Hence area between #-2# and #0# from tables is #0.4772#

and probability is #47.72%#

[See more here.](https://socratic.org/questions/the-area-under-the-normal-curve-between-z-1-0-and-z-2-0#443143)