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Q3. A manufacturer of automobile battieries claims that hte distribution of the lenghts of life of its best bateries has a mean of 54 months and a standard deviation of 6 months. Suppose a consumer group decides to check the manufacturer's claim by purchasing a sample of 50 of those batteries.
a) assuming that manufacturer's claim is true, describe the sampling distribution of the mean lifetime of a sample of 50 battieries.
b) assuming that hte manufacturer's claim is true, what is the probability that the consumer group's sample has a mean life of 52 or fewer months?

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(a) The sampling distribution of the mean life time of the batteries has a mean ...

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