Thousands of batteries are produced every day in a certain manufacturing plant.The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance,like a portable radio or CD player.The quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days.These batteries will be put into a variety of moderately sized appliances and the average of all failure times will be computed.Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries?

A) The uniform distribution
B) The Normal distribution
C) The binomial distribution
D) The Weibull distribution

Question

Thousands of batteries are produced every day in a certain manufacturing plant.The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance,like a portable radio or CD player.The quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days.These batteries will be put into a variety of moderately sized appliances and the average

of all failure times will be computed.Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries?

A) The uniform distribution
B) The Normal distribution
C) The binomial distribution
D) The Weibull distribution

Sebastian Vasquez · Accepted Answer

Final Answer : B, Explanation :  The most appropriate probability distribution to model the average time until failure of these 2000 batteries is the Normal distribution, because the sample size is large enough (n = 2000) to satisfy the Central Limit Theorem, and the data is continuous (time until failure). Additionally, the average value of the failure times can be assumed to be normally distributed due to the Law of Large Numbers.

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