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 20 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 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.
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 20 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 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.
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