Medium sized eggs have a mean weight of 170 ounces with a st

Medium sized eggs have a mean weight of 1.70 ounces with a standard deviation of 0.1 ounces. What is the the value of the mean weight of a carton of a dozen eggs for which only 2% of the cartons will have mean weights larger than?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.98      
          
Then, using table or technology,          
          
z =    2.053748911      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    1.7      
z = the critical z score =    2.053748911      
s = standard deviation =    0.1      
n = sample size =    12      
Then          
          
x = critical value =    1.759286624 [for 1 egg]

As there are 12 eggs here,

12x = critical value for 1 carton = 21.11143949 [ANSWER]