Question

A particular fruit's weights are normally distributed, with a mean of 396 grams and a standard deviation of 29 grams. The heaviest 8% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answer 1

sol ell = 396; 5:29 Heaviest 8-10 => P(Z >2) 0:00 1- P(Z sz) = 0.00 P(Zsz) 1-0.00 P(Z < 2) = 0.92 we in-verse z- table. 1.405 Z = be be Let a fourts weigh 2 ut zo 2= 396 + 1.405 *89 396 +40.745 436.745 a 437 gn CS Scanned with CamScanner

Answer 2

SOLUTION :

Let a grams be the weight  over which 9% fruits are there.

P( x > a) = P( z > (a - m)/s)

=> 0.08 =  P( z > (a - m)/s)

From ND table : 

z > 1.415

The cutoff point is z = 1.415

So, 

a = z * s + m = 1.415 * 29 + 396  = 437 grams

So, the heaviest 8% fruits weigh more than 437 grams (ANSWER).