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A large population of scores from a standardized test are normally distributed with a population mean (μ) of 50 and a standard deviation (σ) of 5. Because the scores are normally distributed, the whole population can be converted into a Z distribution. Because the Z distribution has symmetrical bell shape with known properties, it’s possible to mathematically figure out the percentage of scores within any specified area in the distribution. The Z table provides the percentages corresponding to any Z score. Johns score is 55

d. Tom has a score of 40. What is Tom’s Z score?

e. What is the percentage of students that score lower than Tom?

f. What is the percentage of students that score between John and Tom?

g. Based on the Z table, if 1000 students take the test, how many of them would likely score below Tom’s score?

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