Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.
A. I only
B. II only
C. III only
D. I and II
E. I and III

A. I Only.

Step-by-step explanation:

To begin, we must first be clear that it is the median and that it is the arithmetic mean:

Median is the middle value of a sequence of ordered numbers, for example:

{4,4,4,4,4}, the median is 4 despite being the same numbers.

Now the arithmetic mean is the average value of the samples and is independent of the amplitudes of the intervals.

Then let's analyze each of our options:

I. At least one of the homes was sold for more than $ 165,000.

We know through the flushed:

X1 + X2 +. . . + X7 + (X8 = $130,000) + X9 +. . . + X15 = 15 ∗ 150,000 = $ 2,250,000

Now we will assume the lowest possible value from X1 to X8 = $ 130,000 and from X9 to X15 = X, which is what we want to calculate. That is to say:

X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 130 and X9 = X10 = X11 = X12 = X13 = X14 = X15 = X,

knowing that the total value must be the average of 15, which is equal to $ 2250000 , we have the following equation:

8 ∗ $ 130,000 + 7X = $ 2,250,000

Rearranging:

X = ($ 2,250,000 $ - $ 1,040,000) / 7

X = $ 172,857

Therefore the first statement is true, because at least one house was sold at $ 172,857 which is more than $ 165,000

Evaluating the second option

II. At least one of the homes was sold for more than $ 130,0000 and less than $ 150,000

As the example of the median in the previous case you could have 8 houses that were sold for $ 130,000 or less, therefore here it loses validity, statement II is false.

Evaluating the third option

III. At least one of the homes was sold for less than $ 130,000.

We know that the eighth house sold for $ 130,000, but houses 1 to 7 may also have been sold for that same price. The statement III is false.

Therefore the answer is A. I Only.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

equal to

step-by-step explanation: