A mechanical assembly used in an automobile engine contains four major components. The weights of the components are independent and normally distributed with the following means and standard deviations (in ounces). Component Mean St.Dev. Left case 3 0.2 Right case Bearing assembly Bolt assembly 5 0.5 8 0.1 6 0.5 We consider the total weight of the assembly. (a) What is the probability that the weight of an assembly exceeds 24 ounces? (b) What is the probability that the mean weight, of eight. independent, assemblies

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A mechanical assembly used in an automobile engine contains four major components.
The weights of the components are independent and normally distributed with the
following means and standard deviations (in ounces).
Component
Mean St.Dev.
Left case
3
0.2
Right case
Bearing assembly
Bolt assembly
5
0.5
8
0.1
0.5
We consider the total weight of the assembly.
(a) What is the probability that the weight of an assembly exceeds 24 ounces?
(b) What is the probability that the mean weight of eight independent assemblies
exceeds 24 ounces?
Transcribed Image Text:A mechanical assembly used in an automobile engine contains four major components. The weights of the components are independent and normally distributed with the following means and standard deviations (in ounces). Component Mean St.Dev. Left case 3 0.2 Right case Bearing assembly Bolt assembly 5 0.5 8 0.1 0.5 We consider the total weight of the assembly. (a) What is the probability that the weight of an assembly exceeds 24 ounces? (b) What is the probability that the mean weight of eight independent assemblies exceeds 24 ounces?
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