Answer to Question #320164 in Statistics and Probability for carla

Question

The score of entrance examination takers who took a 600 item exam resemble a normal distribution with a mean of 220 and a standard deviations of 10. The coordinator would like to get the lowest 15% of thr scores and invite them for a retake examination. What range of scores indicates the inclusion in the retake of the exam?

Answer 1

The lower 15% of the normal curve:

$P(Z\leq-1.037)\approx0.15.$

We look for 0.1500 inside the z-table.

Although 0.1500 does not appear, both 0.1492 and 0.1515 do, corresponding to z = -1.04 and -1.03, respectively.

Since 0.1500 is approximately one third way between the two probabilities that do appear, we will use 1.037 as the 15th percentile.

So,

$Z=\cfrac{X-\mu}{\sigma};\\ X=Z\sigma+\mu=1.037\cdot10+220=230.37,$

The range of scores that indicates the inclusion in the retake of the exam is

[0, 230].