The lifetime of a certain type of battery has mean value 12h

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?

Solution

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]