Question

the website for lena’s bank shows these default rates for car loans.
the bank requires the default rate to be less than 5%. lena calculates the default rate using the following steps:
(36 + 42 + 19 + 2) ÷ (102 + 164 + 371 + 587) ≈ 0.081%
lena concludes that the bank’s default rate on car loans is acceptable. is her conclusion correct? explain.

credit score	defaults	total number of loans
551 - 650	42	164
651 - 750	19	371
751+	2	587

a) yes, her work is correct. she found the total number of defaults and divided it by the total number of loans.
b) yes, even though she made a computational error when calculating the default rate.
c) no, because she used the incorrect formula to find the total default rate.
d) no, because she made a mistake when converting the decimal to a percentage.

Explanation:

Step1: Calculate total defaults

$36 + 42 + 19 + 2 = 99$

Step2: Calculate total loans

$102 + 164 + 371 + 587 = 1224$

Step3: Compute correct default rate

$\text{Default Rate} = \frac{99}{1224} \approx 0.0809$

Step4: Convert to percentage

$0.0809 \times 100\% \approx 8.09\%$

Step5: Analyze Lena's error

Lena converted $0.081$ to $0.081\%$ instead of $8.1\%$.

Answer:

D) No, because she made a mistake when converting the decimal to a percentage.