Question

The population of weights of a particular fruit is normally distributed, with a mean of 727 grams and a standard deviation of 20 grams. If 2 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Answer 1

Given that,

mean = = 727

standard deviation = = 20

n = 2

= 727

= / n = 20 / 2=14.14

Using standard normal table,

P(Z > z) = 18%

= 1 - P(Z < z) = 0.18  

= P(Z < z ) = 1 - 0.18

= P(Z < z ) = 0.82

z = 0.92

Using z-score formula  

= z * +   

= 0.92*14.14+727

= 740