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Probability from a Given Situation using Mean

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Brake Pads- A brake pad manufacturer claims its brake pads will last for 38,000 miles. You work for a consumer protection agency and you are testing this manufacturer's brake pads. Assume the life spans of the brake pads are normally distributed. You randomly select 50 brake pads. In your tests, the mean life of the brake pads is 37,000 miles. Assume the standard deviation is 850 miles.

a) Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample is 37,000 miles or less?

b) Using your answer from part (a), what do you think of the manufacturer's claim?

c) Would it be unusual to have an individual brake pad last for 37,000 miles? Why of why not?

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Solution Summary

The solution determines probability from a given situation using mean.

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a) Assuming the claim is correct:
Mean = 38,000
Standard Dev = 850.
Therefore P ( X<= 37000) will be calculated by ...

Solution provided by:
Gaurav Agarwal, MS
Education
  • BE, Bangalore University, India
  • MS, University of Wisconsin-Madison
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