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Determining Battery Lifetime Using Normal Distribution

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A company that manufactures batteries for laptop computers has determined that the average lifetime of its batteries is 360 days with a standard deviation of 30 days. Assuming the lifetime of the batteries is normally distributed, determine the number of days that at least 95% of the batteries will last beyond.

Solution Summary

The solution gives detailed steps on calculating the battery lifetime with known probability under the assumption of normal distribution.

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Probability, Mean

1. A manufacturer of batteries for "kids' toys" wishes to investigate the length of time a battery will last. Tests results on a sample of 10 batteries indicated a sample mean of 5.67 and a sample standard deviation of 0.57.

a. Determine the mean and the standard deviation

b. What is the population mean? What is the best estimate of that value?

c. Construct a 95 percent confidence interval for the population mean.

d. Explain why the t distribution is used as a part of the confidence interval.

e. Is it reasonable for the manufacturer to claim that the batteries will last 6.0 hours? Please provide reasoning for your answer.

2. A cola-dispensing machine is set to dispense a mean of 2.02 liters into a bottle labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters.

a. What is the probability a bottle will contain between 2.02 and 2.04 liters?

b. What is the probability a bottle will contain between 2.00 and 2.03 liters?

c. What is the probability a bottle will contain less than 2 liters?

d. How much cola is dispensed in the largest 4% of the drinks?

3. There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.

a. What is the probability that a candidate is over 60 and female?

b. Given that the candidate is male, what is the probability he is less than 60?

c. Given that the person is over 60, what is the probability the person is female?

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