The shear strength of each of ten test spot welds is determined, yielding the following data (psi):
392 376 401 367 389 362 409 415 358 375
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.
b. Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths.
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).