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?

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%