Answer to Question #216741 in Statistics and Probability for Wacky

Question

The average age of teachers in a certain town is 34 with a standard deviation of
4. If the principal of ABC college employs 100 teachers, find the probability that
the average age of these teachers is less than 35

Answer 1

$\mu=34 \\ \sigma = 4 \\ n=100 \\ P(\bar{x}<35) = P(Z< \frac{35-34}{4 / \sqrt{100}}) \\ = P(Z< 2.5) \\ = 0.9937 \\ = 99.37 \; \%$