Question 759322: Suppose the life of a particular brand of calculator battery is normally distributed with a mean of 75 hours and a standard deviation of 10 hours. If 16 batteries are randomly selected from the population, use Table 4 (Standard Normal probability table), software, or the TI-calculator to find the probability that the sample mean life will be between 70 and 80 hours. Use the Central Limit Theorem.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose the life of a particular brand of calculator battery is normally distributed with a mean of 75 hours and a standard deviation of 10 hours.
If 16 batteries are randomly selected from the population, use Table 4 (Standard Normal probability table), software, or the TI-calculator to find the probability that the sample mean life will be between 70 and 80 hours. Use the Central Limit Theorem.
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t(70) = (70-75)/[10/sqrt(16)] = -5/[10/4] = -20/10 = -2
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t(80) = (80-75)/[10/4] = +2
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P(70< x-bar <80) = P(-2,2,15) = tcdf(-2,2,15) = 0.9361
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Cheers,
Stan H.
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