Lifetimes of one brand of laptop battery life are normally d

Lifetimes of one brand of laptop battery life are normally distributed with a mean of 36 months and a standard deviation of 5 months. Is it unusual for one of those batteries to last only 19 months? Explain by interpreting a z-score. If one battery is selected at random, what is the probability that it will last more than 30 months?

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    19      
u = mean =    36      
          
s = standard deviation =    5      
          
Thus,          
          
z = (x - u) / s =    -3.4      

As this is beyond z = -2, then yes, it is unusual. [ANSWER]

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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 =    30      
u = mean =    36      
          
s = standard deviation =    5      
          
Thus,          
          
z = (x - u) / s =    -1.2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.2   ) =    0.88493033 [ANSWER]