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
