Question

A particular fruit's weights are normally distributed, with a mean of 300 grams and a standard deviation of 7 grams.

The heaviest 15% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

Solution :

Given that ,

mean = = 300

standard deviation = = 7

The z - distribution of the 15% is,

P( Z > z ) = 15%

1 - P( Z < z ) = 0.15

P( Z <  ) = 1 - 0.15

P( Z < z ) = 0.85

P( Z < 1.036) = 0.85

z = 1.036

Using z - score formula,

X = z * +

= 1.036 * 7 + 300  

= 307.25

= 307 gram.