The lifetime of an insulating material tested accelerated te

The lifetime of an insulating material tested (accelerated testing) at 30kV is known to have a mean of 63 hours and standard deviation of 8 hours. A reliability engineer randomly selects n=50 specimens and determines their lifetimes.

a. What is the approximate distribution of X(Standard Diviation) the sample average of the 50 lifetimes? (Use Central Limit Theorem.)

b. Use the result of part (a) to approximate the probability .P(X(SD)>65.20).

Solution

a)

It will have the same mean of 63 hours, and variance of s^2/n = 8^2/50 = 1.28.

Thus, its distribution is N~(63, 1.28).

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    65.2      
u = mean =    63      
          
s = standard deviation =    1.13137085      
          
Thus,          
          
z = (x - u) / s =    1.944543648      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.944543648   ) =    0.025914964 [ANSWER]