question archive Please explain this question for me with step by step explanation if possible: A brake pad manufacturer claims its brake pads will last for 38,000 miles, on average
Please explain this question for me with step by step explanation if possible: A brake pad manufacturer claims its brake pads will last for 38,000 miles, on average
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Please explain this question for me with step by step explanation if possible:
A brake pad manufacturer claims its brake pads will last for 38,000 miles, on average. Assume that the lifespan of the brake pads are normally distributed. Past analyses indicate that (sigma) = 5000 miles. You work for a consumer protection agency and you are testing this manufacturer's brake pads using a random sample of 30 brake pads. In your tests, the mean lifespan of the brake pads you sample is 35,700 miles.
(a)Assuming the manufacturer's claim is correct, what is the probability that the mean lifespan of the sample is as low as 35,700 miles?
(b)What do you think of the manufacturer's claim? Justify
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(a). The probability that the mean lifespan of the sample is as low as 35,700 miles is 0.59%.
(b). The computed z-test result is -2.519524. If the value of alpha is ?α=0.05?, then the region of rejection is above 1.96 or below -1.96. Since -2.519524 < -1.96, then we can reject the null hypothesis of population mean is equal to 38,000 miles. That is, there is no evidence that the manufacturer's brake pads will last for 38,000 miles, on average.
Step-by-step explanation
Given: ?X? follows ?N(38000,50002)?
?X?=35,700? miles
?n=30?
(a). Since X follows a normal distribution, then ?X?? also has an exact normal distribution
?P(X?≤35700)=P(σ/n?X?−μ?≤σ/n?35700−μ?=P(Z≤5000/30?35700−38000?)=P(Z≤−2.519524)=0.005875685?
(b). ?z=σ/n?X?−μ?=5000/30?35700−38000?=−2.519524?
