Determine z-scores and data values for probability distributions.

a. a carpenter measures his work carefully, but his measurements are subject to some naturally occurring error. if his measurements (on average) are off by 0.1 cm, with a standard deviation of 0.09 cm, find the z-score for a measurement that had an error of 0.25 cm. interpret this z-score.

b. assuming the carpenter’s measurement errors are normally distributed, find the measurement error that separates the largest 10% of errors.

c. find the 3rd quartile for the carpenter’s measurement errors.

d. find z0.15