The time (in minutes) that a randomly selected individual waits for an elevator in an office building has a distribution with mean 0.5 and standard deviation 0.289. (a) Let X be the sample mean...

The time (in minutes) that a randomly selected individual waits for an elevator in an office building has a distribution with mean 0.5 and standard deviation 0.289.
(a) Let X be the sample mean waiting time for a random sample of 50 individuals. What are the mean and standard deviation of the sampling distribution of X ?
(b) Approximate P(0.45 ≤ X ≤ 0.57).