Final answer:
To find the probability that a single randomly selected value is greater than 58.2 from a population with a normal distribution, standardize the value and use a standard normal distribution table or calculator to find the area to the right of the standardized value.
Step-by-step explanation:
To find the probability that a single randomly selected value is greater than 58.2, we need to calculate the area under the curve of the normal distribution to the right of the value 58.2.
First, we standardize the value using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, z = (58.2 - 48.1) / 49.4 = 0.204.
Using a standard normal distribution table or a calculator, we find that the area to the right of 0.204 is approximately 0.4192. Therefore, the probability that a single randomly selected value is greater than 58.2 is 0.4192.