The manufacturer of a certain electronic component claims that they are designed to last just slightly...

The manufacturer of a certain electronic component claims that they are designed to last just slightly more than 4 years because they believe that customers typically replace their device before then. Based on information provided by the company, the components should last a mean of 4.24 years with a standard deviation of 0.45 years. For this scenario, assume the lifespans of this component follow a normal distribution.

1. The company offers a warranty for this component that allows customers to return for a refund it if it fails in less than 4 years. What is the probability that a randomly chosen component will last less than 4 years?

2.The company considers a component to be “successful” if it lasts longer than the warranty period before failing. They estimate that about 70.3% of components last more than 4 years. They find a random group of 10 components that were sold and count the number of them which were “successful,” lasting more than 4 years.

What is the probability that at least 8 of these components will last more than 4 years?

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orchestra answered 1 year ago

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