1. The quality control team at a computer technology company needs to estimate the average useful lifespan of their high-end laptops. The useful lifespan looks at how long the laptop will be able to run advanced programs on the market and meet their system specifications. A random sample of 64 laptops indicated a sample average life of approximately 35000 hours with a sample standard deviation of 10000 hours. (25 points)

1. Construct and interpret a 95% CI estimate of the true lifespan of their laptops. (Use 1.96 as the critical value, and use the sample standard deviation as an estimate of population standard deviation)

1. Do you think the company has a right to state that the laptops last an average of 40000 hours? Explain.

1. Does the population need to be normally distributed for the interval to be valid? Explain.

1. Explain why an observed value of 32000 hours is not unusual, even though it is outside the 95% confidence interval you have calculated.

1. Suppose the sample average had been 30000 hours. What would have been your answer to (i)?

1. Now suppose the company wanted a more precise interval estimate. What could they do to narrow the interval estimate?