Question

A normal distribution has a mean of 312.00 and a standard deviation of 26.45. Which interval centered at the mean has a 68% probability of containing a random value drawn from the distribution?

Answer 1

The empirical rule for a normal distribution states that 68% of the data points lie within plus and minus one standard deviation from the mean. Therefore the required interval can be found as follows:
312 - 26.45 = 285.55.
312 + 26.45 = 338.45.
The interval, centered at the mean is (285.55, 338.45)