Question

the accuracy of an automatic pitching machine for batting practice is based on the off-line distance that a pitch is from a target line that is 30m away. the off-line distance is normally distributed with a mean of 0.3 and a standard deviation of 0.05m. what percent of the pitches fall within 0.2m of the target line?

Answer 1

First find the z-score, then use a standard normal table of probabilities

z = (.2 - .3)/.05 = -2
P(z < -2) = .025 or 2.5% (approximately)