A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and σ = 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 MPa be unusually small?

c. If you observed a tensile strength of 20MPa,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 MPa be unusually small?

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