The figure shows the distribution of retail electricity rates in 2007

Question

The figure shows the distribution of retail electricity rates in 2007 for five states in the U.S. in cents per kilowatt hour.

Select from each drop-down menu the option that creates the most accurate statement, given the information provided.

A. If the highest cost range per kilowatt hour is listed for each of the five states included in the figure, then the state with the greatest percentage of customers spending less than six cents per kilowatt hour is .

B. If the average U.S. residential energy customer pays 13.31 cents per kilowatt hour, and every consumer paid the maximum amount per kilowatt hour for each of the ranges listed in the figure, then a randomly selected energy consumer from Massachusetts would be approximately less likely to pay less than the average than is would be a randomly selected energy consumer from Pennsylvania.

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Official Answer

Dropdown 1: Washington Dropdown 2: 97%

IshanSaini · Accepted Answer

Select from each drop-down menu the option that creates the most accurate statement, given the information provided.

A. If the highest cost range per kilowatt hour is listed for each of the five states included in the figure, then the state with the greatest percentage of customers spending less than six cents per kilowatt hour is____________

A. Colorado
B. Mississippi
C. Massachusetts
D. Pennsylvania
 E. Washington

Evident as the only state with the greatest customer fraction in the range.

E. Washington

B. If the average U.S. residential energy customer pays 13.31 cents per kilowatt hour, and every consumer paid the maximum amount per kilowatt hour for each of the ranges listed in the figure, then a randomly selected energy consumer from Massachusetts would be approximately_____________less likely to pay less than the average than is would be a randomly selected energy consumer from Pennsylvania.

A. 9%
B. 33%
C. 66%
 D. 95% 
E. 100%

D. 95%

Right so lets take a step by step approach for this problem.
The stems says that the average is 13.31 cents/ KwHr. Keeping this in memory.
"every consumer paid the maximum amount per kilowatt hour for each of the ranges listed in the figure", this simply means that the question wants us to take the maximum cent/kwhr value of the range.
i.e. 6-8 means 8 cent/kwhr, 12-14 mean 14 cent/kwhr.
OK now we know that we need to find people in the respected country spending less than the average which in our case is 13.3 so 
For the Massachusetts case we can observe about 3% fraction of customers in the 10-12 range that is 3 people in a total of 100 people or 3/100.
Similarly we can observe for Pennsylvania we get about 31 % in 10-12 range and 36% in 8-10 range. This means 31 people in 100 and 36 people in 100 or about 67 people in a total of 200 people are paying less than the average.

Simplify a little bit.
3/100 * 2/2 = 6/200 people from Massachusetts 
while 67/200 people from Pennsylvania .
to see how much is the decrease 67-6 =   *100 = (61/67) * 100 = about 91 % 
Hence IMO D.

Here's my take for this question.

bb · Answer

Official Explanation:

Note that the lowest cost per kilowatt hour listed in the figure is 6-8 cents, so therefore any unaccounted for percentage for any of the listed states must be at a cost of < 6 cents per kilowatt hour, since the questions states that the highest cost range per kilowatt hour is listed for each of the five states.

According to the figure, approximately 100% of the cost range is accounted for each by the bars representing each of Massachusetts, Pennsylvania, Colorado, and Mississippi. However, the only bars for Washington listed are approximately 59% at 6-8 cents per kilowatt hour and approximately 35% at 8-10 cents per kilowatt hour, leaving approximately 6% of the distribution unaccounted for, which must be at a cost less than 6 cents per kilowatt hour.  The correct answer is E

According to the conditions of the problem, approximately 3% of Massachusetts energy customers would pay 12 cents per kilowatt hour and approximately 97% would pay more than the 13.31 cents per kilowatt hour nationwide average. Meanwhile, approximately 31% of Pennsylvania energy customers would pay 14 cents per kilowatt hour and approximately 69% would pay less than the 13.31 cents per kilowatt hour nationwide average.

Now, use the percent change formula to calculate the difference in likelihood of selecting a Massachusetts energy customer paying less than the nationwide average against a Pennsylvania customer paying less than the nationwide average.
Use the calculator to determine that (69 - 3) / 69 = 95.65%.  The correct answer is D

NIMISHAGUPTA · Answer

pls explain OA

yashikaaggarwal · Answer

I can explain Question 1.
But my average answer question 2 is nearby 71%
That is definitely not near to 95%.

Posted from my mobile device

nikitaarora7 · Answer

can someone please explain the second question? what does it mean?
And also post the OA for the same

Rotor666 · Answer

Pls explain the second part, did not really get the stem and solution?

alexmike · Answer

Certainly! Please go ahead and ask any questions or provide more details related to the distribution of retail electricity rates in 2007 for the five states in the U.S. in cents per kilowatt-hour. I'll do my best to assist you based on the information you provide.

Devayusssh · Answer

Did not understand both the parts please explain

Posted from my mobile device

Freddie92 · Answer

What do you suggest if I got this right but it took me 5.20 mins ? Should I be happy with that?

Sajjad1994 · Answer

Not at all! Your time for any single DI question must not go beyond 03:30. If you think any particular question may take more than that; it is better to guess that question within 30 seconds and move on.

cats · Answer

for the second part, why would it be % change

Oppenheimer1945 · Answer

The whole language of the question and arguement is at an issue here.

Gemmie · Answer

A. If the highest cost range per kilowatt hour is listed for each of the five states included in the figure, then the state with the greatest percentage of customers spending less than six cents per kilowatt hour is [Washington].

Meanwhile, the graph already displays the highest score range
=> the remaining of each state's customers not shown in the graphs are those spending < 6 cents/kwh

The graph show % of each state's customers as below

C: \(7 + 80 + 13 = \approx{100}\)
Mis: \(16 + 52 + 32 = \approx{100}\)
W: \(60 + 35 = 95\)
P: \(38 + 32 + 30 = \approx{100}\)
Ma: \(2 + 10 + 50 + 40 \approx{100}\)

=> Washington

B. If the average U.S. residential energy customer pays 13.31 cents per kilowatt hour, and every consumer paid the maximum amount per kilowatt hour for each of the ranges listed in the figure, then a randomly selected energy consumer from Massachusetts would be approximately [97%] less likely to pay less than the average than is would be a randomly selected energy consumer from Pennsylvania.

13.31 is in range 12-14

Ma: only 2% in the range below 12-14 (i.e range 10-12)
P: 70% in the ranges below 12-14 (i.e 38% in range 8-10 and 32% in range 10-12)

Likelihood of pick Mas < Avg: 2%
Likelihood of pick P < Avg: 70%

% difference: \(\frac{(70-2)}{70}=\approx{97%}\)

Adit_ · Answer

Explanation for 1st one is not right. The reason Washington is the answer is because of the fact that Washington only covers roughly <95% above 6 cents/kwh. Thus less than 6 cents/kwh would be over 5%  . This is much more than any other state, as every other state is either 100% close or 97% covered.

vartikg · Answer

CAN ANYBODY EXPLAIN THE STEM TO THE SECOND ONE

Adit_ · Answer

Average is 13.3 cents/kwh. Question is basically asking you to find the percentage of people living in Massachusetts and Pennsylvania that have greater than this 13.3 cents/kwh.

It says each interval is to be assumed as maximum meaning if you have an interval of 6-8 then ALL of them pay 8 cents.kwh. If you have 8-10 interval then ALL pay 10 cents/kwh.
Considering this you need to find the percent of people above 13 cents/kwh? From where do I check this you may ask?
12-14 interval is the start. Why? Because considering our assumption, ALL of them pay 14 cents/kwh in this bracket, and every other interval will also be more than 13 cents/kwh ofcourse.

After you do that you know that paying below average is 100%-(paying above average) so this way you can find the percentage of people below average.
You may ask why I did not directly calculate below average? Because there are some percentages missing as they are BELOW 6. The given graph is not exhaustive.

Then you can calculate individual percentages for both and then compare how much one is with the other one.

Hope it helps.

The figure shows the distribution of retail electricity rates in 2007

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The figure shows the distribution of retail electricity rates in 2007

Prep Toolkit

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