QUESTION 7 Suppose you work for a firm that manufactures a product using raw mat

Question

QUESTION 7 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 5.2 mm and 5.8 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 mean 5.5 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 5.5 mm and a standard deviation of 0.2 mm. Let XB denote the thickness of a metal bracket purchased from supplier B Assuming that supplier A is used, what is the probability that a metal bracket is more than 5.335 mm thick? (Report answer to three decimal places. Answer must be within +- 0.001 of correct value.) QUESTION 8 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 5.2 mm and 5.8 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 mean 5.5 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 5.5 mm and a standard deviation of 0.2 mm. Let XB denote the thickness ofa metal bracket purchased from supplier B. Assuming that supplier A is used, what is the probability that a metal bracket is less than 5.53 mm thick? (Report answer to three decimal places. Answer must be within + o.001 of correct value.)

Explanation / Answer

7)

P(X>5.335)=P(Z>(5.335-5.5)/0.15)=P(Z>-1.1)=0.864

8)

P(X<5.53)=P(Z<(5.53-5.5)/0.15)=P(Z<0.2)=0.579

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