contestada

Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother's score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire's mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance? Claire did better because her Z-score is greater than her mother's. Claire's mother did better because her z-score is greater than Claire's. Claire did better because her z-score is closer to the mean than her mother's. Claire's mother did better because her z-score is closer to the mean than Claire's.

Respuesta :

The z score tells us the number of standard deviations that a given value is from the mean. Recall, standard deviation tells us the spread of the values from the mean

For Claire, the mean score was 510 but she scored 690 which was higher than the mean score

The z score would be

(690 - 510)/110 = 1.63

For Claire's mother, the mean score was 490 but she scored 680 which was higher than the mean score

The z score would be

(680 - 490)/100 = 1.9

We can see that her mother had a higher z score. Compared to the average score, she had a better performance. Therefore, the correct option is

Claire's mother did better because her z-score is greater than Claire's.

Otras preguntas