A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal Distribution with mean μ = 55,000 miles and a standard deviation σ = 4500 miles. The company installs a new brand of brake pads on an SRS of 8 cars. a. If the new brand has the same lifetime distribution as the previous type of brake pad, describe the sampling distribution of the mean lifetime x. Shape:   Mean:    Standard deviation:  b. The average life of the pads on these 8 cars turns out to be x  51,800 miles. Find the probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged.

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  1. A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal Distribution with mean μ = 55,000 miles and a standard deviation σ = 4500 miles. The company installs a new brand of brake pads on an SRS of 8 cars.

a. If the new brand has the same lifetime distribution as the previous type of brake pad, describe the sampling distribution of the mean lifetime x.

Shape:

 

Mean: 

 

Standard deviation: 

b. The average life of the pads on these 8 cars turns out to be x  51,800 miles. Find the probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged.

c. Using your answer from part (b), would you conclude that the new brake pads have the same distribution as the old brake pads? Explain your reasoning.

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