A particular fruits weights are normally distributed with a

A particular fruit\'s weights are normally distributed, with a mean of 725 grams and a standard deviation of 7 grams.

If you pick 21 fruits at random, then 17% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.83      
          
Then, using table or technology,          
          
z =    0.954165253      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    725      
z = the critical z score =    0.954165253      
s = standard deviation =    7      
n = sample size =    21      
Then          
          
x = critical value =    726.4575115 = 726 GRAMS [ANSWER]