(a) (6 pts.) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 98% confidence interval for the population mean of all bulbs produced by this firm. (b) (4 pts.) How large a sample is needed in (a) if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
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a) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. b) How large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
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Madhur L.
A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 1000 hours. This average is maintained by periodically testing random samples of 16 light bulbs. If the $t$ -value falls between $-t_{0.99}$ and $t_{0.99},$ then the company will be satisfied that it is manufacturing acceptable light bulbs. A sample of 16 light bulbs is randomly selected and tested. The mean life span of the sample is 1015 hours and the standard deviation is 25 hours. Assume the life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain your reasoning.
Confidence Intervals
Confidence Intervals for the Mean $(\sigma$ Unknown)
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