Lisa Mendes and Brad Lee work in the sales department of an

Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless Store. Lisa has been signing in an average of 58 new cell phone customers every month with a standard deviation of 28, while Brad signs in an average of 66 new customers with a standard deviation of 19. The store manager offers both Lisa and Brad a $105 incentive bonus if they can sign in more than 105 new customers in a month. Assume a normal distribution to answer the following questions.

a) What is the probability that Lisa will earn the $105 incentive bonus? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

b) What is the probability that Brad will earn the $105 incentive bonus? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    105      
u = mean =    58      
          
s = standard deviation =    28      
          
Thus,          
          
z = (x - u) / s =    1.68      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.68   ) =    0.046478658 [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 =    105      
u = mean =    66      
          
s = standard deviation =    19      
          
Thus,          
          
z = (x - u) / s =    2.05      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.05   ) =    0.020182215 [answer]