A test score above seven hundred

Question

Scores on a standardized test follow a normal (bell-shaped) distribution with a mean of 500 and a standard deviation of 100. What is the probability that a randomly chosen score is above 700?

Accepted Answer

The trick with any normal question is to convert the raw value into a "z-score," which counts how many standard deviations the value sits above the mean: z = \frac{x - \mu}{\sigma}. In words, the z-score rescales the bell curve to a standard one centered at 0 with a spread of 1, so a single table (or memorized fact) covers every normal problem. For x = 700, mean \mu = 500, spread \sigma = 100, z = \frac{700 - 500}{100} = 2. So 700 is exactly 2 standard deviations above average. From the standard normal table, the area to the left of z = 2 is about 0.9772, meaning 97.72% of scores fall below 7…

A test score above seven hundred

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