Question

(c) An aircraft manufacturer purchases a precision assembly for aircraft engines in large lots from a subcontractor. Over time, experience suggests that the assemblies average 5.1 mm in diameter, with a standard deviation of 0.1 mm. (0) If the distribution of diameters of the precision assemblies is bell-shaped (approximately normal), determine the fraction of each lot received from the subcontractor that will possess diameters falling in the interval from 4.9 to 5.3 mm [2 marks] Suppose that the aircraft manufacturer specifies that the assembly diameters must be at least 4.8 mm and not greater than 5.2 mm to be usable in their aircraft engines. Find the fraction of each lot received from the subcontractor that will fail to meet specifications. [3 marks] Page 3 of 3 2010

Answer 1

Here diameters 7 prosion assembly follow normal distribution for moromal avstribution, this Mean M = 5.1 mm Standard deviation (i) standard normal variable २ is giren by 2-M > 2- 3-5.1 ol ni) for a= 419, 2=-2 for 2 = 5:3, a = Required fraction a lot will the poolability 4.93255.3,

Requirred fraction P64955.2) ap (25 *=2) = 2 pes 252) = 2X4773 2x2 2 0.95 45 = 95.45). each Susst fall in Ba-3 Thuy 95.45) iteme 7 I specified interval. (ii) for 22 4.3 1) gives x=521 '' gilles ༣ དུ། fraction of eat eving in 4.8*255.2 boobabirity p(4.84 as 5:2). Thu, is Fraction 7 acceptable parts =P (4.85 x 25.2) ap E3 <3 =1) = Posass) + P(2<3 =1) 0.4987 +23413 Foobyoo =841- 1. Fraction of rejected parts = (180-8477. =16 16) will fail Epecifications. 'The I lot