Question 768269: A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best battery has a mean of 54 months and a standard deviation of 6 months. Recently, the manufacturer has received a number of complaints from unsatisfied customers whose batteries died earlier than expected. A consumer group decides to check the manufacturer's claim by purchasing a SAMPLE of 50 batteries and subjecting them to tests to determine battery life.
Assuming that the manufacturer's claim is true that the mean is 54 and the standard deviation is 6, what is the probability the consumer group's sample will have a mean life of 52 or fewer months?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best battery has a mean of 54 months and a standard deviation of 6 months. Recently, the manufacturer has received a number of complaints from unsatisfied customers whose batteries died earlier than expected. A consumer group decides to check the manufacturer's claim by purchasing a SAMPLE of 50 batteries and subjecting them to tests to determine battery life.
Assuming that the manufacturer's claim is true that the mean is 54 and the standard deviation is 6, what is the probability the consumer group's sample will have a mean life of 52 or fewer months?
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mean of the sample means::: 54 mths
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std of sample means::: 6/sqrt(50) = 0.8485
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z(52) = (52-54)/0.8485 = -2.3570
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P(x-bar < 52) = P(z < -2.3570) = 0.0092
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Cheers,
Stan H.
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