The random variable X is normally distributed. The values 650 and 850 are 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 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
I'd say the answer is D, however in the official answers they say B is larger and the explanation is something like:
"The value 750 is halfway between 850 and 650. However, because the (distribution) curve is decreasing in that interval (the interval after the 50th percentile), the area between 650 and 750 is greater than the area between 750 and 850. Since the value at the 75th percentile should divide in half the AREA between the value at the 60th percentile and the value at the 90th percentile, this value is closer to 650 than to 850."
I've been struggling with this for so long now and believe its wrong what they say. Yes, the AREA between the 60th and 90th percentile should be divided in half at the 75th percentile. However, this can't give me ANY indication about what the variable X will be at the 75th percentile, right?
Thank you very much for any answer!