MEAN DIAMETER OF BALL BEARINGS

A manufacturer of "low precision" 10 mm diameter ball bearings periodically takes samples and measures them to con?rm that the manu- facturing process is still on target. A random sample of 20 ball bearings resulted in diameter measurements with an average of x¯ = 9.86 mm, and a standard deviation s = 1.01 mm. Postulating that the random sample X1 , X2 ,..., X20 is from a Gaussian distribution with μ = 10, ?nd the probability that any sample mean, X¯ , will fall to either side of the postulated mean by the observed amount or more, by chance alone. i.e. P (X¯   ≤ 9.86) or P (X¯   ≥ 10.14).