A statistics exam was given. Calculate the percentile for each of the following four students.
a. Johnâ€™s z-score was 21.62.
b. Maryâ€™s z-score was 0.50.
c. Zakâ€™s z-score was 1.79.
d. Friedaâ€™s z-score was 2.48.
Are the following statements true or false? Explain your reasoning.
a. â€œIf we see a standardized z-value beyond 63, the variable cannot be normally distributed.â€
b. â€œIf 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.â€
c. â€œTwo machines fill 2-liter soft drink bottles by using a similar process. Machine A has Î¼ 5 1,990 ml and Ïƒ 5 5 ml while Machine B has Î¼ 5 1,995 ml and Ïƒ 5 3 ml. The variables cannot both be normally distributed since they have different standard deviations.â€