6. -/4 points DevoreStat9 6.E.025. My Notes The shear strength of each of ten te

Question

6. -/4 points DevoreStat9 6.E.025. My Notes The shear strength of each of ten test spot welds is determined, yielding the following data (psi). 67 415 362 358 381 37 409 375 389 363 (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 psi standard deviation 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 ? and ?? 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(XS 400)-0((400-?)/?).] (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help? eadtT Talk to a Tutor

Explanation / Answer

The statistical software output for this problem is:

Summary statistics:

Hence,

a) Mean = 379 psi

Standard deviation = 19.75 psi

b) z score for 95% area to its left = 1.645

Hence,

Required strength = 379 + 1.645*19.75 = 411.49 psi

c) P(X < 400)

= P(z < 1.06)

= 0.8562

Column Mean Std. dev. Data 379 19.748418

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