Question

If m is the median of x, then what does the expression p(x≤m)=0.4 indicate?

1) The probability of a randomly chosen value from x being greater than the median is 0.4
2) The probability of a randomly chosen value from x being less than the median is 0.4
3) The probability of a randomly chosen value from x being equal to the median is 0.4
4) The probability of a randomly chosen value from x being not equal to the median is 0.4

Answer 1

The expression p(x≤m)=0.4 indicates that the probability of a randomly chosen value from x being less than or equal to the median is 0.4, so option 2 is correct.

Step-by-step explanation:

If m is the median of x, then the expression p(x≤m)=0.4 indicates that the probability of a randomly chosen value from x being less than or equal to the median is 0.4. This means that 40% of the values in the distribution are below or equal to the median. Therefore, the correct interpretation of the expression is that the probability of a randomly chosen value from x being less than the median is 0.4, which corresponds to option 2.

It is important to note that for a continuous random variable, the probability of the variable taking on any single specific value, like the median itself, is zero. Hence, we cannot say that the probability of a value being exactly equal to the median is 0.4 (referencing option 3), nor does the expression address the probability of being greater than or not equal to the median (options 1 and 4).