Author Question: Suppose the mean GMAT score is 550 with a standard deviation of 100 . Hayden takes the GMAT and is ... (Read 113 times)

CharlieWard · **on:** Aug 1, 2018

Suppose the mean GMAT score is 550 with a standard deviation of 100 . Hayden takes the GMAT and is told his z-score is 2.5 . Interpret the meaning of a z-score in this context.

Question 2

In 1998, the average age of students at UTC was 22 with a standard deviation of 3.96 . In 1999, the average age was 24 with a standard deviation of 4.08 . In which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

nguyenhoanhat · **Reply #1 on:** Aug 1, 2018

Answer to Question 1

Since Hayden's z-score is positive, he scored above the mean of 550 . The value, 2.5, indicates he scored 2.5 standard deviations from the mean. One standard deviation is 100, so 2.5 standard deviations is 250 . Therefore, Hayden scored 250 points above the mean of 550, or 800 on the GMAT.

Answer to Question 2

Coefficient of Variation for 1998 = 18
Coefficient of Variation for 1999 = 17
Since 18 > 17, 1998 shows a more dispersed distribution.