The lifetime of a certain resistor in a certain application has a mean of 900 hours and a standard deviation of 30 hours. Four resistors are used in sequence (i. e., one after the other), and the total length of time that the four resistors last is recorded. The resistors are independent of one another. What is the mean length of time in hours that the four resistors last?

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Mathematics

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13 May, 21:32

The lifetime of a certain resistor in a certain application has a mean of 900 hours and a standard deviation of 30 hours. Four resistors are used in sequence (i. e., one after the other), and the total length of time that the four resistors last is recorded. The resistors are independent of one another. What is the mean length of time in hours that the four resistors last?

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Alexis Krause · Answer 1

The mean of the 4 resistor sample will be equal to the mean of the whole population too.

Step-by-step explanation:

The mean (μₓ) and standard deviation of the sample mean (σₓ) are related to the mean (μ) and standard deviation of the population (σ) through the following relationship

μₓ = μ = 900 hours

σₓ = σ/√n = 30/√4 = 30/2 = 15 hours