Please help. Thank you in advance for your time.
In an English class last semester, Foofy earned a 76 (x¯= 85, Sx= 10). Her
friend, Bubbles, in a different class, earned a 60 (x¯= 50, Sx = 4). Should Foofy
be bragging about how much better she did? Why?
To determine if Foofy should be bragging about how much better she did compared to her friend Bubbles, we need to analyze their grades using the concept of z-scores.
A z-score measures how many standard deviations a particular value is from the mean of a set of data. To calculate the z-score, we need to know the mean (x¯) and standard deviation (Sx) of the data set.
For Foofy:
Mean (x¯) = 85
Standard Deviation (Sx) = 10
Foofy's grade = 76
To calculate the z-score for Foofy's grade, we use the formula:
Z = (x - x¯) / Sx
Plugging in the values:
Z for Foofy = (76 - 85) / 10
Now, let's calculate the z-score for Bubbles:
Mean (x¯) = 50
Standard Deviation (Sx) = 4
Bubbles' grade = 60
Z for Bubbles = (60 - 50) / 4
Once we calculate the z-scores for both Foofy and Bubbles, we can compare their values. The z-score measures how many standard deviations each grade is from its respective mean.
If the z-score is positive, it means the grade is above the mean, while a negative z-score indicates the grade is below the mean.
So, if Foofy's z-score is higher than Bubbles' z-score, it means she performed better relative to the rest of her class compared to Bubbles in her class.
Therefore, to answer the question of whether Foofy should be bragging about performing better, we need to compare their z-scores. If Foofy's z-score is higher (closer to 0) than Bubbles' z-score, then yes, she can rightfully claim better performance. If not, she may not have performed significantly better.
By calculating the z-scores based on the given information, we can determine if Foofy has a valid reason to brag or not.
To determine whether Foofy should be bragging about doing better than Bubbles, we can compare their scores using the z-score formula.
The z-score formula is calculated using the following formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the individual score
- μ is the population mean
- σ is the population standard deviation
Let's calculate the z-scores for both Foofy and Bubbles:
For Foofy:
x = 76
μ = 85
σ = 10
z_Foofy = (76 - 85) / 10
z_Foofy = -0.9
For Bubbles:
x = 60
μ = 50
σ = 4
z_Bubbles = (60 - 50) / 4
z_Bubbles = 2.5
The z-scores represent the number of standard deviations away from the mean each student's score is. A positive z-score indicates a score that is above the mean, while a negative z-score indicates a score below the mean.
In this case, Foofy's z-score is -0.9, meaning her score is approximately 0.9 standard deviations below the mean for her class. On the other hand, Bubbles' z-score is 2.5, suggesting that her score is roughly 2.5 standard deviations above the mean for her class.
Based on the z-scores, it can be concluded that Bubbles performed better relative to her class mean than Foofy did. Foofy's score is below the mean, while Bubbles' score is well above the mean. Therefore, Foofy should not be bragging about doing better than Bubbles since Bubbles performed significantly better in comparison.