Q2. Proportions (percentages) in a ZDistribution

A large population of scores from a standardized test arenormally distributed with a population mean (?) of 50 and astandard deviation (?) of 5. Because the scores are normallydistributed, the whole population can be converted into a Zdistribution. Because the Z distribution has symmetrical bell shapewith known properties, it’s possible to mathematically figure outthe percentage of scores within any specified area in thedistribution. The Z table provides the percentages corresponding toany Z score.

a. John has a score of 55. What is John’s Z score?

b. What is the percentage of students that score lower thanJohn?

c. Based on the Z table, if 1000 students take the test, howmany of them would likely score above John’s score? (Round theanswer to a whole number)

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

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

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

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

h. Anna scores at the 99^th percentile on this exam,what is her Z score?

Hint: A score at 99^th percentile means 99% of thescores are below this score.

i. Based on the result of the previous question, what is Anna’sactual score on the exam?

j. What would be the median score on this exam?

Hint: Review the definition of “median” and then figure outthe percentage of scores below (or above) this score.