Question

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

3) 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.

a. What is the expected number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.)

b. What is the standard deviation for the number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.)

c. What is the probability that no more than 6 of these components will last more than 4 years?

4) The company is not satisfied with how many returns they are processing, and accountants in the company are recommending that they change the warranty period. The accountants suggest basing the period of the warranty on making sure, in the long run, only about 5% of customers will return the component. What amount of time corresponds to the shortest 5% of lifespans for this component? (Round your answer to 1 decimal place.)

Answer 1