Refer to the Anti-Corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of oil field pipes, Exercise 2.46. Recall that a scanning probe instrument was used to measure the surface roughness x (in micrometers) of 20 sampled sections of coated interior pipe. Consider the sample mean, x.

a. Assume that the surface roughness distribution has a mean of μ = 1.8 micrometers and a standard deviation of σ = .5 micrometer. Use this information to find the probability that x exceeds 1.85 micrometers.

b. The sample data are reproduced in the following table. Compute x.

c. Based on the result, part b, comment on the validity of the assumptions made in part a.

1.72 2.50 2.16 2.57 2.64 1.26 2.13 1.06 2.24 2.31 2.03 1.09 1.40 2.05 1.19 2.13 1.27 1.51 2.41 1.95