Question

A particular fruit's weights are normally distributed, with a mean of 527 grams and a standard deviation of 40 grams.

If you pick 11 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

µ =    527                              
σ =    40                              
n=   11                              
proportion=   0.8                           
                                  
Z value at    0.89   =   1.227      (excel formula =NORMSINV(   0.89   ) )          
z=(x-µ)/(σ/√n)                                  
so, X=z * σ/√n +µ=   1.227   *   40   / √    11   +   527   =   541.792

If you pick 11 fruits at random, then 11% of the time, their mean weight will be greater than 542 grams