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. What proportion of students had a higher score than Amanda? Use your z table. Question 6 options: 0.10 0.32 0.18 0.82

Answer 1

In math notation, we've done this: z = (X - μ) / σ = (940 - 850) / 100 = 0.90 where z is the z-score X is Vivian's score (940) µ is the mean (850) σ is the standard deviation (100) As you may know, in a normal distribution it's expected that about 68% of all observations will fall within 1 standard deviation of the mean, 95% will fall within 2 standard deviations, and 99% will fall within 3 standard deviations. 
940 lie before the first standard deviation, in which 16.5% is above it
since 940 is 0.9 from the mean and 0.1 from the first standard deviation
so above it is 17.5 % = 0.175 or about 0.18