Question

A particular fruit's weights are normally distributed, with a mean of 747 grams and a standard deviation of 5 grams.

The heaviest 8% of fruits weigh more than how many grams?

Give your answer to the nearest gram..

Answer 1

Solution :

Given that ,

mean = = 747

standard deviation = = 5

The z - distribution of the 8% is,

P( Z > z ) = 8 %

1 - P( Z < z ) = 0.08

P( Z <  ) = 1 - 0.08

P( Z < z ) = 0.92

P( Z < 1.405) = 0.92

z = 1.405

Using z - score formula,

X = z * +

= 1.405 * 5 + 747  

= 754.025

= 754 gram