A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). $$\begin{array} { | l | c | c | c | c | c | }
\hline \text { Interest Rate } & 7.0 \% & 7.5 \% & 8.0 \% & 8.5 \% & 8.5 \% \
\hline \text { Probability } & 0.12 & 0.23 & 0.24 & 0.35 & 0.06 \
\hline
\end{array}$$ If a bank is selected at random from this distribution,what is the chance that the interest rate charged on a home loan will exceed 8.0%?
A) 0.59
B) 0.06
C) 1.00
D) 0.41

Question

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Interest Rate } & 7.0 \% & 7.5 \% & 8.0 \% & 8.5 \% & > 8.5 \% \
\hline \text { Probability } & 0.12 & 0.23 & 0.24 & 0.35 & 0.06 \
\hline
\end{array}$$ If a bank is selected at random from this distribution,what is the chance that the interest rate charged on a home loan will exceed 8.0%?
A) 0.59
B) 0.06
C) 1.00
D) 0.41

Quizplus · Accepted Answer

To find the probability of the interest rate being charged exceeding 8.0%, we need to add up the percentages for the four categories that exceed 8.0%: 8.01%-8.25%, 8.26%-8.5%, 8.51%-8.75%, and 8.76%-9.0%. This gives us a total percentage of 41.1% (24.3% + 11.3% + 4.1% + 1.4%). Therefore, the probability of the interest rate being charged exceeding 8.0% is 0.411 or approximately 0.41. The correct answer is D.

A Recent Survey of Banks Revealed the Following Distribution for the Interest