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When the manufacturing process is working properly, the distribution of battery lifetimes has mean μ = 17 hours with standard deviation σ = 0.8 hour, and 73% last at least 16.5 hours.

1.) Assume that the manufacturing process is working properly, and let p^ = the sample proportion of batteries that last at least 16.5 hours. Calculate the mean and standard deviation of the sampling distribution of p^ for random samples of 50 batteries.

2.) Describe the shape of the sampling distribution of p^ for random samples of 50 batteries. Justify your answer.

3.) In the sample of 50 batteries, only 68% lasted at least 16.5 hours. Find the probability of obtaining a random sample of 50 batteries where p^ is 0.68 or less if the manufacturing process is working properly.

4.) Assume that the process is working properly, and let x bar = the sample mean lifetime (in hours). Calculate the mean and standard deviation of the sampling distribution of x bar for random samples of 50 batteries.

5.) Describe the shape of the sampling distribution of x bar for random samples of 50 batteries. Justify your answer.

6.) In the sample of 50 batteries, the mean lifetime was only 16.718 hours. Find the probability of obtaining a random sample of 50 batteries with a mean lifetime of 16.718 hours or less if the manufacturing process is working properly.

7.) Based on your answers to Questions 3 and 6, should the company be worried that the manufacturing process isn’t working properly? Explain

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