Final answer:
To find the probability that a randomly selected x-value from a normal distribution is in a given interval, we need to calculate the z-scores corresponding to the endpoints of the interval and use a standard normal distribution table or calculator.
Step-by-step explanation:
To find the probability that a randomly selected x-value from a normal distribution is in a given interval, we need to calculate the z-scores corresponding to the endpoints of the interval. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
In this case, we have a mean of 58 and a standard deviation of 2. Let's say the interval is (a, b). We need to find the z-scores z1 and z2 for a and b, respectively. Once we have the z-scores, we can use a standard normal distribution table or a calculator to find the probability.
So, the probability that a randomly selected x-value from the distribution is in the given interval is P(a < x < b) = P(z1 < z < z2), where P(z1 < z < z2) can be found using a standard normal distribution table or a calculator.