Answer:
a) In this case, we have a z-score of 1.57, characterized as:
This signifies that our score is 1.57 standard deviations above the average of all test scores.
b)
Using the normal standard distribution or Excel, we computed:
This represents 2.275% of the dataset.
Step-by-step explanation:
Previous concepts
Normal distribution denotes a "probability distribution that is symmetric around the mean, indicating that data close to the mean occurs more frequently than data further from it".
The Z-score serves as "a statistical measurement representing a value's relation to the average (mean) of a set, calculated in terms of standard deviations away from the mean".
Solution to the problem
Part a
For this instance, we hold a z-score of 1.57, which is defined as:
This shows that our score is 1.57 deviations above the overall test score average.
Part b
A z-score of z=-2 indicates that your friend's score is 2 deviations below the other test scores.
Assuming a normal distribution, we can derive the percentage:
Using the normal standard distribution or Excel, we discovered:
This represents 2.275% of the data.