Question

Amanda earned a score of 940 on a national achievement test that was normally distributed. The mean test score was 850 with a standard deviation of 100. If 1000 students took the test, how many scored below Amanda? Use your z table.

Answer 1

First, to find out the number of students who scored below Amanda, we must find the z-score value of Amanda's score using the formula below.

$Z = \frac{(\chi - \mu)}{\sigma}$

where Z is the z-score, Χ is the expected average value, μ is the mean of Χ, and δ is the standard deviation. Thus, we have

$Z = \frac{(940 - 850)}{\sqrt{100}}$
$Z = 0.90$

Thus, using the z-table, we have P(Z<0.90) = 0.8159. Since we have wanted to find the number of students who scored below Amanda, then from the whole, we have (1 - 0.8159) = 0.1841. That means, out of 1000 students, 0.1841 of them scored below Amanda. Thus, we have (0.184)(1000) = 184. 

Answer: 184 students