Question

in a recent survey, it was found that the median income of families in country a was $57,300. what is the probability that a randomly selected family has an income less than $57,300?

what is the probability that a randomly selected family has an income less than $57,300?

(type an integer or a decimal.)

Explanation:

Step1: Recall the definition of median

The median divides a data - set into two equal parts. Half of the data values are less than or equal to the median and half of the data values are greater than or equal to the median.

Step2: Calculate the probability

If \(M = 57300\) is the median of the income distribution of families in country A, and we assume a continuous distribution (for simplicity, in the context of probability, when dealing with a median in a population - level measure), the probability \(P(X<57300)\) is given by the proportion of the population with income less than the median.

Since the median splits the distribution into two equal parts, if \(X\) is the random variable representing family income, then \(P(X < 57300)=\frac{1}{2}\)

Answer:

\(0.5\)