A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with \(\mu=5\) and \(\sigma=0.5\). Let \(X\) be the strength of a randomly sampled specimen of this composite.

a. If the claim is true, what is \(P(X<20)\) ?

b. Based on the answer to part (a), if the claim is true, would a strength of \(20 \mathrm{MPa}\) be unusually small?

c. If you observed a tensile strength of \(20 \mathrm{MPa}\), would this be convincing evidence that the claim is false? Explain.

d. If the claim is true, what is \(P(X<130)\) ?

e. Based on the answer to part (d), if the claim is true, would a strength of \(130 \mathrm{MPa}\) be unusually small?

f. If you observed a tensile strength of \(130 \mathrm{MPa}\), would this be convincing evidence that the claim is false? Explain.