A machine manufactures bolts that are supposed to be 3 inches in length. Each day a quality engineer selects a random sample of 50 bolts from the day’s production, measures their lengths, and performs a hypothesis test of H0: µ = 3 versus H1: µ ≠ 3 where µ is the mean length of all the bolts manufactured that day. Assume that the population standard deviation for bolt lengths is 0.1 in. If H0 is rejected at the 5% level, the machine is shut down and recalibrated.

a. Assume that on a given day, the true mean length of bolts is 3 in. What is the probability that the machine will be shut down? (This is called the false alarm rate.)

b. If the true mean bolt length on a given day is 3.01 in., find the probability that the equipment will be recalibrated.

Section 3.1 STAT 250 David Holmes FEB 13 Numerical Summaries of Center and Variation Three characteristics of a numerical variable’s distribution: • Shape • Center (Typical Value) • Spread (Variability) Can a few numerical measures be used to describe a distribution’s entire shape NO Graphs provide the best overall picture of a distribution....