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In a manufacturing process that laminates several ceramic layers, 1% of the assembles are defective. Assume that the assemblies are independent.
a) What is the mean number of assemblies that need to be checked to obtain 5 defective assemblies?
b) What is the standard deviation of the number of assemblies that need to be checked to obtain 5 defective assemblies?
X = number of assemblies needed to obtain 5 defectives.

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taskmasters
There are several information's already given in the question. based on those information's, the answer can be easily deduced.

a. It is already given that 1% are defective. It is required to find the number that is needed to be checked to get 5 defective products.
Then
1% of X = 5
0.01X = 5
x = 5/0.01
   = 500

b. σ = square root [(n^2−1)/12]
       = square root [(250000 - 1)/12]
       = square root [249999/12]
       = square root (20833.25)
       = 144.34
       = 144
I hope the procedure is clear enough for you to understand. I also hope that this is the answer that you were looking for and the answer has actually come to your desired help.

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