a set of maths exame score mean is 70 and variance is 8. a set of english score has mean is 74 and variance is 16. for which exame whould a score of x=78 have a higher standing?
Standard deviation (SD) = square root of variance
Z = (score-mean)/SD
Whichever Z score is the highest.
To determine which exam a score of x=78 would have a higher standing in, we need to compare the z-scores for each exam. The z-score measures how many standard deviations a particular score is from the mean.
To calculate the z-score, use the formula:
z = (x - μ) / σ
Where:
- x is the score you want to compare (x=78 in this case)
- μ is the mean score of the exam
- σ is the standard deviation of the exam
Let's calculate the z-scores for the Math and English exams:
For the Math exam:
Mean (μ) = 70
Standard Deviation (σ) = √8 ≈ 2.83
z_math = (78 - 70) / 2.83 ≈ 2.83
For the English exam:
Mean (μ) = 74
Standard Deviation (σ) = √16 = 4
z_english = (78 - 74) / 4 = 1
Comparing the two z-scores, we find that the z-score for the Math exam (z_math ≈ 2.83) is higher than the z-score for the English exam (z_english = 1). Therefore, a score of 78 would have a higher standing in the Math exam.