A statistics exam was given. Calculate the percentile for each of the following four students.

a. John’s z-score was 21.62.

b. Mary’s z-score was 0.50.

c. Zak’s z-score was 1.79.

d. Frieda’s z-score was 2.48.

Are the following statements true or false? Explain your reasoning.

a. “If we see a standardized z-value beyond 63, the variable cannot be normally distributed.”

b. “If X and Y are two normally distributed random variables measured in different units (e.g., X is in pounds and Y is in kilograms), then it is not meaningful to compare the standardized z-values.”

c. “Two machines fill 2-liter soft drink bottles by using a similar process. Machine A has μ 5 1,990 ml and σ 5 5 ml while Machine B has μ 5 1,995 ml and σ 5 3 ml. The variables cannot both be normally distributed since they have different standard deviations.”

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