Question

A particular fruit's weights are normally distributed, with a mean of 256 grams and a standard deviation of 9 grams.

The heaviest 5% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

solution

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.64 ) = 0.95

z = 1.64 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.64*9+256

x= 270.76

x=271