1 Employees in GMs Lake Orion assembly plant worked an avera

1. Employees in GM\'s Lake Orion assembly plant worked an average of 118.56 hours of overtime last year with a standard deviation of 25.85 hours. Determine the z-score for a simple random sample of 35 time sheets (from the past year) that produces an average of 114.00 hours.

2. Employees at Excel Carwash worked an average of 118.59 hours last month with a standard deviation of 31.10 hours. Determine the z-score for a simple random sample of 53 time sheets (from the past month) that produces an average of 115.00 hours.

Solution

1.

We get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    114      
u = mean =    118.56      
n = sample size =    35      
s = standard deviation =    25.85      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.043610205   [ANSWER]

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2.

We get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    115      
u = mean =    118.59      
n = sample size =    53      
s = standard deviation =    31.1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.840372814   [ANSWER]