(Solved): A population of values has a normal distribution with \( \mu=218.5 \) and \( \sigma=47.3 \). If a r ...

A population of values has a normal distribution with \( \mu=218.5 \) and \( \sigma=47.3 \). If a random sample of size \( n=25 \) is selected, a. Find the probability that a single randomly selected value is greater than 214.7. Round your answer to four decimals. \[ P(X>214.7)= \] b. Find the probability that a sample of size \( n=25 \) is randomly selected with a mean greater than 214.7. Round your answer to four decimals. \[ P(M>214.7)= \]