The shear strength of each of ten test spot welds is determined, yielding the following data (psi)

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The shear strength of each of ten test spot welds is determined, yielding the following data (psi).

389

405

409

367

358

415

376

375

367

362

(a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.)

average		382.3  psi
standard deviation		20.8 psi

(b) Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [Hint: What is the 95th percentile in terms of μ and σ? Now use the invariance principle.] (Round your answer to two decimal places.)

________________________psi

(c) Suppose we decide to examine another test spot weld. Let X = shear strength of the weld. Use the given data to obtain the mle of P(X ≤ 400). [Hint:

P(X ≤ 400) = Φ((400 − μ)/σ).]

(Round your answer to four decimal places.)

___________.

please show steps!!!