Eldon received 72 on his first calculus test. The marks were normally distributed with a mean of 60 and a standard deviation of 8. He received 80 on the next test, which was normally distributed with a mean of 75 and a standard deviation of 6. Which was the better mark, relatively speaking?
z value of 1st test = [72-60]/8 = +1.5
z value of 2nd test = [80-75]/6 = +0.83
Thus the 1st test mark is better
is this right ??
To determine which mark was better, relatively speaking, we can compare the scores using standard deviation units. This allows us to understand how far each score is from the mean in terms of the variability of the data.
First, let's calculate the z-score for each test score using the formula:
z = (x - μ) / σ
where:
z is the z-score,
x is the test score,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
For the first calculus test:
x1 = 72
μ1 = 60
σ1 = 8
Using the formula, we can calculate the z1-score:
z1 = (72 - 60) / 8
z1 = 12 / 8
z1 = 1.5
For the second calculus test:
x2 = 80
μ2 = 75
σ2 = 6
Using the formula, we can calculate the z2-score:
z2 = (80 - 75) / 6
z2 = 5 / 6
z2 ≈ 0.8333
Now, let's compare the z-scores. A higher z-score indicates a relatively better mark compared to the mean.
In this case, Eldon's first calculus test score has a z1-score of 1.5, while his second calculus test score has a z2-score of approximately 0.8333.
Since 1.5 > 0.8333, Eldon's first calculus test score of 72 was relatively better compared to his second calculus test score of 80.