4 a car company has found that the lifetime of its

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4. A car company has found that the lifetime of its batteries varies from car to car according to a Normal distribution with mean µ = 48 months and a standard deviation σ = 7.7 months. The company installs a new brand of battery on an SRS of 9 cars. a. If the new brand has the same lifetime distribution as the previous type of battery, describe the sampling distribution of ´ x . b. The average life of the batteries on these 8 cars turns out to be ´ x = 42.3 months. Find the probability that the sample mean lifetime is 42.3 months or less if the lifetime distribution is unchanged. What conclusion would you draw? 5. What sample size would be required to reduce the standard deviation of the sampling distribution to one- third the value you found in 3. Justify your answer. 6. Harley-Davidson motorcycles make up 13% of all motorcycles registered of all the motorcycles registered in the United States. You plan to interview an SRS 450 motorcycle owners. How likely is your sample to contain 19% or more who own Harleys? Show your work.
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