145. The article “Response of SiCf/Si3N4 Composites Under Static and Cyclic Loading—An Experimental and Statistical Analysis” (J. Engrg. Materials Tech., 1997: 186 –193) suggests that tensile strength (MPa) of composites under specified conditions can be modeled by a Weibull distribution with a  9 and b  180.

a. Sketch a graph of the density function.

b. What is the probability that the strength of a randomly selected specimen will exceed 175?

Will be between 150 and 175?

c. If two randomly selected specimens are chosen and their strengths are independent of one another, what is the probability that at least one has a strength between 150 and 175?

d. What strength value separates the weakest 10%

of all specimens from the remaining 90%?