annual per capita consumption of fresh apples in lbs in near

annual per capita consumption of fresh apples (in lbs) in nearby state can be approximated by normal distribution

mean is 16.8 lbs

std dev is 3.5 lbs

what is the smallest annual per capita consumption of apples that can be in the top 25% of consumption?

and in the top 15% of consumption?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.75      
          
Then, using table or technology,          
          
z =    0.67448975      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    16.8      
z = the critical z score =    0.67448975      
s = standard deviation =    3.5      
          
Then          
          
x = critical value =    19.16071413   [answer, top 25%]

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First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.85      
          
Then, using table or technology,          
          
z =    1.036433389      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    16.8      
z = the critical z score =    1.036433389      
s = standard deviation =    3.5      
          
Then          
          
x = critical value =    20.42751686   [answer, top 15%]