A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and a 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.

Step 1 of 7</p>

Let X be the strength of the composite

Here the claim is the tensile strength is has a lognormal distribution with and

X follows the lognormal distribution with mean

And standard deviation =0.5

Step 2 of 7</p>

a) We have to find if the claim is true

=

We have to find the Z score for 2.9957

Then Z=

=(2.9957-5)/0.5

= -4.0086

Now P(X<20)=P(Z< -4.01)

=0.00003

Hence P(X<20)=0.00003

Step 3 of 7</p>

b) Yes, The strength of 20 MPa is unusually small

Because this occurs 3 in 100000 samples

Step 4 of 7</p>

c) Yes this the convincing evidence that the claim is false

Because the probability is very small

And the strength of 20 MPa is unusually small