Question: Surface roughness of pipe. Refer to the Anti-Corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of oil field pipes, Exercise 2.46 (p. 62). Recall that a

scanning probe instrument was used to measure the surface roughness x (in micrometers) of 20 sampled sections of Coated interior pipe. The data are saved in the ROUGHPIPE

file. Consider the sample mean, \(\bar{x}\) .

1. Assume that the surface roughness distribution has a mean of \(\mu \) = 1.8 micrometers and a standard deviation of \(\sigma \) = .5 micrometer. Use this information to find the probability that \(\bar{x}\) exceeds 1.85 micrometers.
2. The sample data are reproduced in the following table. Compute \(\bar{x}\).
3. Based on the result, part b, comment on the validity of the assumptions made in part a.

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