A microchip manufacturer has determined that 6% of the processors they produce are defective. A quality technician performs the experiment of having each unit from an assembly line inspected until a defective unit is found. When a defective unit is found, the assembly line's production will be stopped. What is the expected value for the number of inspections until a defective unit is found

Question

Mathematics

Taylor Merritt

3 October, 11:25

A microchip manufacturer has determined that 6% of the processors they produce are defective. A quality technician performs the experiment of having each unit from an assembly line inspected until a defective unit is found. When a defective unit is found, the assembly line's production will be stopped. What is the expected value for the number of inspections until a defective unit is found

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Lana Ibarra · Answer 1

The expected value for the number of inspections until a defective unit is found 17.

Step-by-step explanation:

Percentage of defective microchips = 6%

Let the total number of inspection = x

number of defective microchip = 1

As we know

1/x = 6%

1/x = 0.06

x = 1 / 0.06

x = 16.67 inspections

x = 17 (rounded off to nearest whole number)

17 inspection is done until the defective microchip is found.