Many U.S. railroad tracks were built using A7 steel, and there is renewed interest in the properties of this metal. The article “Stress-State, Temperature, and Strain Rate Dependence of Vintage ASTM A7 Steel” (J. Engr. Mater. Tech. 2019) describes, among other things, the distribution of manganese within A7 steel specimens. The authors found that the nearest-neighbor distance (NND, in microns) of manganese particles along longitudinal planes in A7 steel follow a Weibull distribution with (approximate) parameter values α = 1.18 and β = 21.61.
a. What is the probability of observing a NND between 20 and 40 lm? Less than 20 lm? More than 40 lm?
b. What are the mean and standard deviation of this distribution?
c. What is the median of this distribution?