Suppose you work for a firm that manufactures a product using raw materials and several components that are purchased from other companies. One of these components, a metal bracket, is especially critical with respect to its thickness. The specifications for the metal bracket require that its thickness be between 5.3 mm and 5.9 mm. One of your duties is to purchase the metal brackets from a supplier. Two suppliers (Supplier A and Supplier B) are competing for your business.
Supplier A produces metal brackets such that the thickness of any given bracket is a normal random variable having a mean of 5.6 mm and a standard deviation of 0.15 mm. Let XA denote the thickness of a metal bracket purchased from Supplier A. Supplier B produces metal brackets such that the thickness of any given bracket is a normal random variable having a mean of 5.6 mm and a standard deviation of 0.2 mm.
Let XB denote the thickness of a metal bracket purchased from Supplier B. Compute the following probabilities assuming that Supplier A is used:
(a) the probability that a metal bracket is less than 5.6 mm thick
(b) the probability that a metal bracket is more than 5.33 mm thick
(c) the probability that a metal bracket is more than 5.8 mm thick Compute the following values assuming that Supplier B is used:
(d) the thickness that is exceeded by 50% of metal brackets
(e) the thickness that is exceeded by 90% of metal brackets
(f) the value that exceeds the thickness of 95% of metal brackets
(g) upper and lower thickness values, symmetric about the mean, that contain the values of 99% of metal brackets