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.
Step-by-step explanation:
The difference quotient represents the slope of the line connecting two points on a curve. To achieve the most accurate estimate, we need to use points that are nearest to x = 0. For this problem, the relevant points are (-0.001, 1.999) and (0.001, 2.001).
m = (2.001 − 1.999) / (0.001 − (-0.001))
m = 1
To calculate the monthly interest, take the APR and divide it by 360, then multiply the result by 30 days. Typically, each loan is backed by the vehicle that was purchased, hence we will utilize the secured APR.
8. For an average secured APR of 5.85%, the calculation is: 5.85% divided by 360 multiplied by 30 gives a monthly rate of 0.4875%.
The vehicle cost is 19,725; with a sales tax of 4.75% and a down payment of 2,175.
19,725 multiplied by 1.0475 results in 20,661.94, and after subtracting the down payment, the loan amount is 18,486.94.
To find the accrued interest for the first month: 18,486.94 multiplied by 0.4875% equals 90.12.
9. An excellent secured APR of 4.80% results in a monthly rate of 0.40% when 4.80% is divided by 360 and multiplied by 30.
Price of a different vehicle: 15,867; a sales tax of 5.25%; down payment equals 10% of the total.
Calculating, 15,867 multiplied by 1.0525 gives 16,700.02; taking 90% results in a principal balance of 15,030.02 at the loan's beginning.
10. For a fair secured APR at 7%, dividing by 360 and multiplying by 30 provides a monthly rate of 0.5833%.
Cost of a new vehicle is 19,072; sales tax stands at 4.5%; down payment of 1,200.
Cost for a used vehicle is 15,365; same tax and down payment as the new one.
Calculating for new: 19,072 multiplied by 1.045 results in 19,930.24, with down payment deducted gives 18,730.24.
Accrued interest for new is 18,730.24 multiplied by 0.5833% equating to 109.25.
For the used vehicle: 15,365 multiplied by 1.045 results in 16,056.43, then down payment leaves 14,856.43.
Accrued interest here is 14,856.43 multiplied by 0.5833% equaling 86.66.
The difference in interest accrued by the first month's end is 109.25 minus 86.66, which is 22.59.
