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.

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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. [latex] Z = \frac{(\chi - \mu)}{\sigma} [/latex] 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 [latex] Z = \frac{(940 - 850)}{\sqrt{100}} [/latex] [latex] Z = 0.90 [/latex] 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

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