Question

Steel rods are manufactured with a mean length of 23 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normal distributed with a standard deviation of 0.08 Click the icon to view a table of areas under the normal curve (a) What proportion of rods has a length less than 22.9 cm? 0.0478 (Round to four decimal places as needed) (b) Any rods that are shorter than 22 87 om or longer than 23.13 om are discarded. What proportion of rods will be discarded? (Round to four decimal places as needed)

Answer 1

0.06 solutim! Let X~ N(M= 23,00.06) a) P(x< 22,9) = P(XCM < 2204-23 ) = P(Z <-1.67) = P(Z >167) /prx 222-1) = 0.0575 {fon table 1 b) P(x<22.87 . *> 23-13) =P(x<22.87)+P(x>23-137 -P(x22287,xx287) = P(422287-23 )+P 2318-23)-16). = Plz<-2.17)+P(z>2:17)-0 = P(27217) +P6272.17) = 2Plz>2.172 - 260.015003.) strom table? PX 222.87 A x>23:13 ) = 0.0300