sandy wrote:
The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
Quantity A |
Quantity B |
The value at the 75th percentile of the distribution of X |
750 |
VERY tricky question.
When it comes to normal distributions, it might be useful to think of the area under the curve as the ENTIRE population being examined.
In fact, it helps more of you think of each blue pixel/dot under the curve as representing one member of the population.
this explanation was super helpful.
The halfway point between scores is flat, and can be equal, but if you drew a line from the 750 score to its percentile, it would have to be less than halfway between 650 and 850, since the curve curves downward, with less area.
So, if a score of 650 is at the 60th percentile, we know that 60% of all of the blue pixels/dots lie to the left of 650
Likewise, if a score of 850 is at the 90th percentile, we know that 90% of all of the blue pixels/dots lie to the left of 850
IMPORTANT: If we draw a new line that takes the population BETWEEN the 60th and 90th percentiles and divides that population into two EQUAL populations, then that new line will represent the 75th percentile score.
So, where should that line go?
Well, if we draw it halfway between 650 and 850...
...then more of the population will be on side A.
So, this line will NOT divide the population between the 60th and 90th percentiles into two equal populations.
To get a line the DOES divide the population into two equal populations, we need to draw it right about here...
Notice that the 75th percentile line is to the left of score of 750 (which is halfway between scores of 650 and 850)
So, the SCORE associated with the 75th percentile is LESS THAN 750
Answer: B