A company that manufactures treadmills provides a full warra

A company that manufactures treadmills provides a full warranty for one year after the point of sale. It knows that 10% of its treadmills are defective. However, it also knows that only 30% of their customers will use the treadmill within the first year after the point of sale. If the company expects to sell 600 treadmills next year, what is the probability that more than 5% of the total number of treadmills sold will be returned for service under its warranty?

Solution

Let

D = defective
U = use in first year
R = return

Thus,

P(R) = P(U) P(D|U) = 0.30*0.10 = 0.03

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.05      
u = mean = p =    0.03      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.006964194      
          
Thus,          
          
z = (x - u) / s =    2.871832634      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.871832634   ) =    0.002040495 [ANSWER]