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?

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?

dumbcow · Answer

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)