Final answer:
To find the probability that a randomly selected family has an income greater than $57,300, we can use the z-score formula and the normal distribution.
Step-by-step explanation:
To find the probability that a randomly selected family has an income greater than $57,300, we need to know the shape of the income distribution. Assuming the distribution is normal, we can use the z-score formula to calculate the probability. First, we need to find the z-score of $57,300 using the mean and standard deviation of the income distribution. Then, we can use the z-table or a calculator to find the corresponding probability.
For example, let's say the mean income is $60,000 and the standard deviation is $10,000. The z-score of $57,300 would be:
z = (57,300 - 60,000) / 10,000 = -0.27
Using the z-table or calculator, we can find that the probability of a randomly selected family having an income greater than $57,300 is approximately 0.3944, or 39.44%.