A manufacturer claims that the life span of its tires is 52 comma 00052,000 mile
ID: 2947005 • Letter: A
Question
A manufacturer claims that the life span of its tires is
52 comma 00052,000
miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select
100100
tires at random and test them. The mean life span is
51 comma 79951,799
miles. Assume
sigma?equals=700700.
Complete parts? (a) through? (c).
?(a) Assuming the? manufacturer's claim is? correct, what is the probability that the mean of the sample is
51 comma 79951,799
miles or? less?
nothing
?(Round to four decimal places as? needed.)
?(b) Using your answer from part? (a), what do you think of the? manufacturer's claim?
The claim is
?
because the sample mean
?
be considered unusual since it
?
within the range of a usual? event, namely within
?
1 standard deviation
2 standard deviations
3 standard deviations
of the mean of the sample means.?(c) Assuming the? manufacturer's claim is? true, would it be unusual to have an individual tire with a life span of
51 comma 79951,799
?miles? Why or why? not?
?
No
Yes
?, because
51 comma 79951,799
?
lies
does not lie
within the range of a usual? event, namely within
?
1 standard deviation
2 standard deviations
3 standard deviations
of the mean for an individual tire.
Explanation / Answer
a)probability that the mean of the sample is less than 51799=P(Xbar<51799)=P(Z<(51799-52000)/(700/sqrt(100))
=P(Z<-2.87)=0.0021 ( please try 0.0020 if this comes wrong)
b)The claim is wrong;because the sample mean can be be considered unusual since it
does not lie within the range of a usualnamely within 2 standard deviationsof the mean of the sample means.
c)
No because 51,799 lie within the range of a usual vent, namely within 2 standard deviations of the mean for an individual tire.
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