Question

The population of weights of a particular fruit is normally distributed, with a mean of 709 grams and a standard deviation of 39 grams. If 20 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Answer 1

Solution :

Given that ,

mean = = 709

standard deviation = = 39

n = 20

= = 709

= / n = 39 / 20 = 8.7207

The z - distribution of the 2% is,

P( Z > z ) = 2 %

1 - P( Z < z ) = 0.02

P( Z <  ) = 1 - 0.02

P( Z < z ) = 0.98

P( Z < 2.054) = 0.98

z = 2.054

Using z - score formula,

X = z * +

= 2.054 * 8.7207 + 709

= 726.9123

= 727 grams