The lifetime of a certain type of battery has mean value 12hours and standard de
ID: 3379005 • Letter: T
Question
The lifetime of a certain type of battery has mean value 12hours and standard deviation 1 hour. There are 36 batteries in a package.
a) By central limit theorem, the average _______ will be normally distributed.
A. Lifetime of any randomly selected ALL batteries in a package (36 counts)
B.Lifetime of ALL batteries of this certain type
b)What lifetime value is such that the average lifetime of ALL batteries in a package exceeds that value for only 5% of all packages? (hint: to find a VALUE)
c)What lifetime value is such that the TOTAL lifetime of ALL batteries in a package exceeds that value for only 5% of all packages?
Explanation / Answer
a)
A. Lifetime of any randomly selected ALL batteries in a package (36 counts)
[The central limit theorem talks about samples, not individuals, so it is OPTION A.]
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b)
First, we get the z score from the given left tailed area. As
Left tailed area = 0.95
Then, using table or technology,
z = 1.644853627
As x = u + z * s / sqrt(n)
where
u = mean = 12
z = the critical z score = 1.644853627
s = standard deviation = 1
n = sample size = 36
Then
x = critical value = 12.27414227 [ANSWER]
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c)
Multiplying the critical value in (b) to get the total lifetime of 36 batteries,
critical sum = 12.27414227*36 = 441.8691217 [ANSWER]
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