Question

Alen scored 18 in the Mid-Term Test (N(16,1.5)) and got 89 in the Final Exam (N(78,9.5)). Which did he do better, the Mid-Term Test or the Final Exam?

Answer 1

To compare Alen's performance on the Mid-Term Test and the Final Exam, we can calculate the z-scores for each score. The z-score tells us how many standard deviations away from the mean the score is. By comparing the z-scores, we can determine which test Alen did better in.

Step-by-step explanation:

To determine which test Alen did better in, we need to compare his scores on the Mid-Term Test and the Final Exam. Alen scored 18 in the Mid-Term Test, which follows a normal distribution with a mean of 16 and a standard deviation of 1.5. He got 89 in the Final Exam, which follows a normal distribution with a mean of 78 and a standard deviation of 9.5.

To compare the two scores, we can calculate the z-scores for each. The z-score tells us how many standard deviations away from the mean the score is. The formula for z-score is: z = (x - mean) / standard deviation. Plugging in the values, we can calculate:

Mid-Term Test z-score = (18 - 16) / 1.5 = 2 / 1.5 = 1.33

Final Exam z-score = (89 - 78) / 9.5 = 11 / 9.5 = 1.16

Since the Mid-Term Test z-score is higher than the Final Exam z-score, Alen did better in the Mid-Term Test.