Question

The mean score of a college entrance test is 500; the standard deviation is 75. the scores are normally distributed. what percent of the students scored below 320?

Answer 1

To find the percentage of students who scored below 320 we proceed as follows:
σ=75
μ=500
the z-score of this information is given by:
z=(x-μ)/σ
thus the z-score when x=320 will be:
z=(320-500)/75
z=-2.4
thus:
P(x<320)=P(z=-2.4)=0.0082~0.82%
Thus:
Answer: 0.82%